I went a bit down the rabbit hole with this one, I had some idea but in the end I ended up reading quite a lot about early chromatic harmonicas and diatonic harmonicas, so see if my ideas were in fact justified. I hope you'll excuse the long answer, but in my opinion it's all relevant to why the instrument is the way it is today, and imho it's pretty interesting for a harmonica player too.
So, in order to understand why the chromatic harmonica is tuned the way it is, it's necessary to understand a bit about the harmonica tunings in general. First off, what is conventionally thought of as the "chromatic harmonica" tuning, is more "properly" known as the "solo tuning".
For background, by far the most common tuning for the harmonica in the west is the tuning used since the mid-1800s for 10 hole diatonics (popularised by the Hohner Marine Band). This is commonly referred to as the "richter system" (although strictly speaking this refers to a family of tunings, it's generally understood that "richter tuning" refers to the below layout when not otherwise qualified):
1 2 3 4 5 6 7 8 9 10
blow: |C |E |G |C |E |G |C |E |G |C |
draw: |D |G |B |D |F |A |B |D |F |A |
The point of the Richter tuned 10 hole diatonic harmonica was this: a compact, affordable, intuitive instrument that would play folk/dance melodies, a simple chordal accompaniment, and allow a skilled played to do both at the same time. Essentially, to perform the role an instrument like the anglo concertina might play, but cheaply, and in your pocket.
In the end, a series of "happy accidents" discovered by black American musicians at the turn of the century came to redefine the sound of the diatonic harmonica, and the way the instrument is played today has almost nothing to do with what the instrument was originally designed for. Chromaticism via bends, 2nd position playing, wailing, microtonally inflected melodies: absolutely none of this was a factor in the design, but nowadays constitute the core vocabulary of the instrument.
Because of how wildly successful these innovations in playing technique have been (and later ones too), it's easy to forget just how good the Richter tuning is at the original purpose for which it was designed. This style of playing, playing folk melodies alongside a concertina-like accompaniment, is rarely if ever encountered today. Archetypical example (obligatory oh Susanna) here:
So far this might seem unrelated to the chromatic harmonica, but bear with me: the other thing that's great about the Richter tuning is that you can easily harmonise melodies. When playing a melody in the home key, at least one (usually both) of the adjacent notes are viable harmonies. This can either a) be used judiciously and skilfully to embellish melodies with a harmony line or b) cover your arse if you're not the most accurate player. Most players fall somewhere in between, but intuitiveness this layout produces is useful even for skilled players: the only "clash" on the instrument is between the A and the B, and even that can actually be really nice in a lot of contexts. An absolutely charming example of this style of playing, what you might call "embellished melodic playing" is found here.
Now, if you're playing with an accompaniment, especially with another free reed instrument like a squeezebox or another harmonica, you might not care that much about the chords in the lower end. In that case, you're going to be playing single note melodies and melodies in thirds (and perhaps the occasional note cluster for embellishment). In that case, it starts to become "a bug not a feature" that the A and F are missing in the bottom octave. You can see how, in the above example, while he does use the bottom end chords occasionally, not much would be lost if those chords were compromised, in favour of a complete major scale.
For this reason a new tuning called "solo tuning" was invented at the turn of the 20th century. Derived from the Richter tuning it was optimised for playing as a "soloist"; as chiefly a melodic instrument. The problem is, of course that you have a 7 note scale which you're trying to fit into a system of pairs of holes. Either you're going to have a repetition, or the blows and draws will get out of sync. Solo tuning gets around this by taking the major scale from the middle of the 10 hole Richter tuning (holes 4-7) and repeating it through the whole instrument, (i.e. repeating the C and having a reversal in breath patterns in the last 2 holes).
So, what was:
1 2 3 4 5 6 7 8 9 10
blow: |C |E |G |C |E |G |C |E |G |C |
draw: |D |G |B |D |F |A |B |D |F |A |
In solo tuning becomes:
1 2 3 4 5 6 7 8 9 10… etc.
blow: |C |E |G |C |C |E |G |C |C |E...etc.
draw: |D |F |A |B |D |F |A |B |D |F...etc
Why might this be useful? Take this recording here
The bottom octave of the harmonica is almost completely neglected because of its missing notes: and because of this, the player is using a low tuned harmonica (a ten whole richter in D but every note 1 octave down) and just neglecting the first few holes altogether, essentially treating it as a 7 holed instrument. It's easy to see how a better alternative for this melodic playing might be a solo tuned harmonica, allowing for a greater range on the instrument.
Now, there are a couple of other obvious options they could have gone for, as have been alluded to in the question and comments:
1) regular breath, repeated C
1 2 3 4 5 6 7 8 9 10 11 12(...)
blow: |C |E |G |B |C |E |G |B |C |E |G |B (...)
draw: |D |F |A |C |D |F |A |C |D |F |A |C (...)
2) no repetition
1 2 3 4 5 6 7 8 9 10 11(...)
blow: |C |E |G |B |D |F |A |C |E |G |B (...)
draw: |D |F |A |C |E |G |B |D |F |A |C (...)
For the second option, yes it's more efficient because there's no superfluous note, but it means you have to learn a completely different breathing pattern in the middle octave. And while conceptually it's just the same thing backwards, practically I imagine it would leave your "muscle memory" pretty damn confused.
Now the top one may look very logical indeed: it has a regular breathing pattern throughout the harmonica for one. However, you lose the ability to play stabs of the tonic chord (unless you're really damn careful), and you gain the possibility of a horrible semitone clash. It's called the "harmonica" for a reason, it's supposed to be harmonious! So the conventional solo tuning wins out: despite the awkward turnaround, you have a big C major chord, and no terrible clashes.
Now, why is this relevant to the chromatic harmonica? I don't have a source to hand for this, but I think it's reasonable to say that the chromatic harmonica was not designed to be an instrument to play in all keys, but to simply give the player the option of playing additional chromatic notes where required within certain keys. In the modern world, chromatics are large, expensive instruments with valves, 16 holes, complex slider assemblies, and hefty price tags. The first ever chromatic harmonica though, the Hohner Chromonica 260, looks like this:
Now, it seems pretty clear to me that this was not intended to be an all singing, all dancing, fully chromatic instrument. It was merely intended to add the "missing" notes to the existing diatonic instrument, so that should you run into a melody that included the occasional chromatic note, you could still play it. I'm not sure if there are any sources that explicitly state this was the intention of the manufacturer, but as evidence to this, the Hohner chromonica was first offered in RICHTER tuning, and offered in all 12 keys. That's right, the first chromatics were not in solo tuning at all, but richter!
An example of this type of harmonica can be heard here:
Notice that if it wasn't for the slide ornaments, you would never guess from the tone that this is a chromatic harmonica: the less bulky construction, and the lack of valving means that these harps essentially sound like diatonics ("throaty") not chromatics ("reedy"). The tuning means you still have chordal possibilities, but some missing notes.
Only later were chromatics made in the solo tuning, the first being a 12 hole variant (initially called the chromonica 270 and then later the "super chromonica"). This later acquired valves, and became the template for the modern chromatic. According to Pat Missin, you can find catalogues even into the 1950s which specify that the chromonica is available in either "regular" (meaning richter) or "solo" tuning. Hohner were still selling Richter tuned valveless diatonics in the form of the Hohner Koch until a few years ago! (although this was by this time niche instrument).
Despite the original intention though, the C major solo tuned harmonica has obvious parallels with the piano; it can be thought of as a "white key" harmonica with a "black key" slider. I could be wrong here, but I believe it was really Larry Adler who in the 1930s started treating the instrument as a "serious" chromatic instrument, playing all sorts of arrangements of classical music on a C major solo tuned chromatic (without transposing the original music). Adler really was an evangelist for the chromatic harmonica, and changed the perception of the instrument in both the minds of the public and the marketing materials from manufactures. And so the "classical" harmonica player was born!
Although this is changing with the resurgence of the 10 hole diatonic, post-war I think it's fair to say that, in general, chromatic harmonicas were successfully marketed as the "serious" and "respectable" cousins of their diatonic counterparts. Like a jazz guitar purist who (stupidly) scoffs at the idea of ever using a capo to transpose, you do find classical harmonica players who are scornful of the idea of a diatonic player who needs to change harmonicas to play a song in another key, and even MORE scornful of a chromatic player who requires multiple keys of the instrument to play all of their repertoire. Another factor is that since chromatic harmonicas have become more and more advanced, they've also become more and more expensive, which leads most players to want to use a C chromatic for all pieces. However, I think it's a mistake to think that the instrument was designed with this philosophy in mind.
So there you have it: the reason the chromatic harmonica is tuned the way it is because it's a pretty OK tuning to play folk tunes in C major on it, in a style that is rarely played today. It's a fundamentally anachronistic layout which is not optimised for and was never designed as a fully chromatic instrument, and often makes life MUCH more difficult than it needs to be. Working around the difficulties caused by the layout is sometimes seen as the badge of a "true" chromatic harmonica player by purists, but the layout of the instrument has undeniably had a huge influence on the repertoire written and arranged for the harmonica, as certain patterns in certain keys are impossibly difficult.
So why does it persist? This is a subjective question: there are players who will argue tooth and nail that the current layout is superior to any alterations. In my opinion though, it's simply inertia: it's just "the way it is". The question is, are there better options? There are multiple considerations that you might care about in a note layout: regularity of breathing pattern, the distribution of enharmonic notes, differences in scale patterns between keys, chordal possibilities, and doublestops. This is leaving out all the layouts which don't aim for chromaticism at all: slide diatonics for example.
A variety of different tuning systems exist which aim to produce a more logical chromatic note layout. Some attempt to remove the idea of a "home key" altogether so that all keys are equally playable and scale patterns are the same in each key (like isomorphic keyboards do, for example on accordions). Others are non-uniform across all keys, but still have "the edge taken off" when compared to the traditional solo tuning.
The most conservative (and common) adjustment is the "bebop" tuning, which changes one of the duplicated Cs to a Bb. The most divergent tuning that has a fair amount of use is the diminished tuning, which is completely isomorphic: scale patterns are the same in every key, and all notes have a double stop a minor third above them. One of the more interesting and I think promising ones is the major sixth tuning, sometimes known as "power chromatic" after Brendan Power, this might fairly be described as a "compromise" tuning: it still has a "home key", and some major chords, but it's more flexible and versatile than the traditional solo tuning because of the regular breathing pattern, more equitable distribution of enharmonic notes, and uniformity of blow/draw intervals (1 tone).
Whether these will catch on, who can say. Personally I think there's a good chance they will, as, unlike with ideas such as the janko keyboard
, a harmonica is 1) a personal instrument not a communal one and 2) more often than not, self-taught 3) completely opaque to the observer so autodidacts use their ears not their eyes not to learn it 4) not too difficult to customise yourself.
If you have any interest in trying new layouts for either the chromatic or the diatonic, reeds can be reversibly retuned by judiciously adding little blobs of blue tack to the reeds. It sounds like a joke, but it's a common practice that works incredibly well. I've even gigged with blue tacked harps! A more permanent solution is blobs of solder.