A slash chord like B♭/C is read as "B♭ over C". The first thing that comes to mind is "B♭" and then "C". That makes sense for inversions, like C/E or Cm/G, because the structure of interest is indeed the C or Cm in this case, dictating the harmony. However it seems to me that it should be the opposite when dealing with more complex slash chords. B♭/C is not some kind of "B♭" chord, but it's heard as some kind of "C" chord. When we play this structure (a bass note with a major triad one whole step down on top) we are looking for a particular sonority, in this case a kind of suspended dominant sound. My point is that it makes more sense to read and think as "C with B♭ on top" (maybe there is something more elegant, since english is not my native language) because the root is the first thing that should come to mind. This makes it easier to learn the sounds and theory of these structures as unique entities (for example: if you want this specific sound of suspended dominant chord, you stack a major triad a whole step down on top of your root; if you want a specific lydian sound, stack a minor triad one half step down on top of your root, ...). Do you see any drawbacks to the use of this reasoning?
English is my first language, and I can't think of any better way to put it than you already have! The way you've described these more complex slash chords is exactly how I think of them. When I see
B♭/C, I think
C7sus. When I see
Bmin/C, I think
Cmaj#11. Thinking about it from an educational / pedagogical perspective, when working with a new student, it probably makes most sense to teach these chords initially as
Cmaj#11, for the very reasons you mention. Then when teaching the particular voicings, one could point out to the student that he/she can achieve the desired harmony simply by playing a major triad a whole step below the root, etc. In charts, I would initially expose new students only to the true harmony (
C7sus, etc.) and not the triad shortcuts for voicing those chords. Then when those students encounter a song with something like
B♭/C, they will recognize it as a particular way to voice
In short, I can only think of advantages to the approach you've described! Before studying harmonies more thoroughly, I remember encountering slash chords like
G♭/A and wondering what the true harmony was. It felt like I hadn't been given enough information, and I was very restricted in my soloing because I didn't recognize the true harmony and the chord chart didn't state it. Your approach would remove this sort of uncertainty.
I tend to think the same. Bb/C contains Bb D F and C. So could be construed as Bb add 9 or Bb add 2. Or C9 sus 4. Even C11. When I see it written as a slash chord, it makes me think is there a better way to write it, but there probably isn't. It makes sense physically - Bb triad, but bass note is a tone higher, although musically maybe it belongs more with C than Bb - it may depend on whether the slash is a passing note, or part of a series of block chords, as in 'Midnight at the Oasis'.
The topmost chord symbol (e.g. Bb in Bb/C, or Cm in Cm/G) represents at least 2 notes, often 3 or more. It doesn't represent just one note, so I don't like thinking of Bb/C as "C with Bb on top" (IMO, this wording comes dangerously close to thinking of both of those as note names whenever the chord symbol is also a note name, simply because it's unfamiliar and I don't think I'm the only one who defaults to assuming that things are note names in unfamiliar contexts).
I tend to think of slash chords as "Topmost Chord in right hand, put bottom note in left hand". I am too lazy to analyze the music theory behind a new lead sheet, especially if I need to sight read it now--I just want to play the music, and I don't want to reanalyze the chords to fit what some of the other answerers hear (at least, not now).
The logic behind the convention of having the lowest note under/behind the slash is quite durable. For a start, it is consistent with the way things are expressed mathematically and with our conception of high and low pitch. C/D or 'C over D' suggests over and under, high and low.
It is true that we must start with some assumptions: pianists have to learn that higher notes lie to the right, or 'up' the keyboard, and players of stringed instruments need to learn that 'up the neck' means towards the body of the instrument. It is true that quite a few of my students are initially confused about left and right, high and low on the instrument and high and low pitch, but once they get over this bump they can operate in a high-low, up-down musical world (flautists are a special case, but that's the way they like to be treated). The connection between left, low on the instrument and low pitch is strengthened (at least in english) by the fact that they all start with the letter 'l'.
Yes, there are inconsistencies. We notate the accidental before the note, yet name it C sharp or D flat, but by turning the slash chord convention on its head, as it were, we would be adding another inconsistency.