I play guitar and trombone. This question does not concern me, but why don't more instruments with a wider range of notes (e.g. pianos) use alto clef? With C on the middle line, it makes so much sense. So, why not?
Yes! It is criminal that C clefs aren't taught more.
But first, the rationale for C clefs. Here is middle C shown in treble, soprano, mezzo-soprano, alto, tenor, baritone, and bass clefs:
Since sopranos will be singing above middle C, their middle C is correspondingly the lowest of the C clefs to give all the staff space above middle C. In this way, the C clef minimizes the need for leger lines. The same is true of baritone clef (the final C clef above); since baritones mostly sing below middle C, middle C is placed highest in the staff to minimize the need for leger lines.
As ttw says, the lack of alto clef is partly tradition and partly convenience. (I'll add one more: partly ignorance, because most musicians don't know them!) But I think that all C clefs should be taught to serious practicing musicians, and here's why:
We saw above that a C can occupy seven distinct spots on the staff. And since there are seven pitches, this has incredible potential for helping students transpose.
- Imagine you're a flute player, and all you have is a B-flat clarinet part. Since the clarinet is a transposing instrument, the B-flat you see on the clarinet part is actually a C. So what is your flute player to do? Just stick an alto clef in front and mentally change the key signature. Now suddenly they can read the exact same part as the clarinet, but they're transposing on the fly without really knowing it.
Long story short, since C can occupy all seven spots on the staff thanks to C clefs, fluent knowledge of C clefs allows you to immediately transpose to any pitch level.
I utterly disagree with the other opinions. The alto clef is not a superior device that is just underused because of unfortunate historical accident. Rather, it is particularly hard to read because it signifies almost but not quite the same thing as the common clefs (treble and bass).
To explain: the alto clef puts a C on the middle line. By itself, that's okay - pitch values and line position are obviously not intrinsically related, but only by arbitrary convention. So by itself it makes sense to anchor your scale wherever it allows you to get away with the fewest ledger lines.
But there's the rub: the alto clef is not used by itself. Almost everyone uses treble and bass clefs - even if you're a lifelong viola player, you'll almost certainly have started learning to read music via the more common clefs. And both of those put the C between two lines - in fact, right below or right above the middle line.
This makes is much harder that it has to be to sight-read melodic lines, because your entire mental model of the scale shifts around: in the alto clef, a C in the staff is now on a line rather than between lines, a D is between lines rather than on a line, and so on for the entire scale. This would be no problem if people read music by consulting the clef at the beginning of the line and then doing the math - but that's not how gestalt perception works. Most of the time, a musician will not even look at the clef on the far left side, but simply remember which type it was. We don't calculate quantities, we recognize shapes. And recognizing a shape when all the local indicators for what a pitch looks like are inverted is hard, because a lot of useful heuristics that your visual system could otherwise exploit simply don't work.
Disclaimer: I say this as an organist who frequently has to read all three clefs at the same time. It's so much harder than it has to be, it isn't even funny. In almost every case I would much prefer it if the middle system used a modern clef, no matter how many ledger lines it takes.
The usual violin/bass split piano note system is centered around middle C, and a single system would be quite awful for representing the total range piano scores navigate for everything but the simplest kinds of music.
Others point to "tradition" but that's not just a red but a bright orange herring: in olden times ledger lines were not being used and consequently there were wagonloads of different clefs for numerous instrument ranges (cf LilyPond's "modern" clefs most of which were still in use in baroque times, and also look for "mensural clefs".
That nowadays we have economized on a quite smaller number of clefs is making it easier for musicians to exchange parts between instruments and for conductors to read scores fluently and for music teachers to demonstrate instrumentalist parts on the piano.
There are a few exceptions of course, viola being one where the score/fingering connection when using the alto clef is closer to what a violin does than, say, an octavated violin clef would provide. Using the alto clef for that reason is nicer for crossfiddlers than many other options (granted, a mezzosoprano clef would be even nicer, but then we get into clef proliferation again).