What a mess. Have there ever been any serious efforts toward “modernizing” musical notation?
To give you an idea of how not-a-problem it is, many composers (myself included) prefer to read orchestral scores (so, a page will have roughly 15-20 staves) that are transposed. So, instead of reading each instrument in the same key, we see what each player is reading. If the concert key is C, I'll see the clarinets and trumpets reading in D, etc. I prefer it because you get a better sense of how the music feels to each individual player, and can better respond to any issues they're having.
It's a mess to look at, I guess, but to any reasonably well trained musician, it's clear as day and conveys far more useful information than the "cleaner" way of seeing everyone in the same key, which really just obfuscates what's really going on.
Those things you mentioned actually make perfect sense when you arrive at them with the following assumptions/understandings:
-Western music is founded (not limited to, but founded) on the concept of a "tonal center."
-Western music is founded (again, not limited to, but certainly founded on) limiting the number of available pitches to those available in the equal temperament system, which is to say that the distance between the smallest internal, a half-step, is equal. This means that no tonal centers, or "keys," are favored by the tuning system. In the past certain keyboards might have been tuned to favor pieces written in G, for example. On a "G keyboard," a 5th from G to D would actually be a different number of cents than a 5th from, say, D to A (more on that in a moment).
-Western music also tends to like returning to said tonal centers. Going away from it -- tension, and returning -- release. It's emotionally satisfying and, while I'm only really barely scratching the surface, this concept can explain a lot.
With all this in mind, the "octave" thing makes sense, because for whatever reason, humans like to resolve to tonal centers in a similar fashion -- the basic culmination of all of this is a major key, which no matter what your tonal center is, can be created by starting at a note (let's say C for simplicity), and then counting up the following interval pattern: WWHWWWH, where W = whole step, and H = half step. Therefore, the key of C is C D E F G A B (and then C to complete the final half-step at the top, but we already said that tone so it doesn't need to be included -- but, C to C is 8 notes!).
If the tonal center (or "tonic") is C#, then your major scale is spelled C# D# E# F# G# A# B#. This can answer your B/B#/C question: yes, from the "perspective" of a major scale in the key of C, which unfortunately is what most "layman" musicians tend to think of when they think of a scale due to where music education usually starts, then yes, no B# exists, and the "gap" seems in-congruent, inconsistent, a flaw in the system, like something was bolted on to make it work. But from the "perspective" of C#, then not only does a B# exist, but so does an E#! It's actually a very elegant and, I guess you could say, "self-correcting" system. The lack of a B# from the "C major perspective" is actually a fault of our tendency to start there, but is also an inevitable outcome of a system that is designed to treat all keys equally.
If anything, Western music terminology has a "tonality" bias, which is true, and might be what you're running into and what is confusing you. Once you start really stretching the limits (but this stuff really isn't at all pertinent to this discussion, or really what most people would generally like to listen to...it tends to mostly exist in academic circles), the limitations of the terminology become obvious. But mostly, it perfectly reflects what the vast majority of our music is.
The only thing I'm not quite getting from your post is bringing up backwards compatibility. I get the sense that you're trying to express a fuzzy concept and are arriving at the nearest programming terminology, but I'm not sure what that concept is. Backwards compatibility doesn't really make any sense in the context of harmony. If anything, it technically breaks backwards compatibility with music written before equal temperament was fully adopted, since music written using other tuning systems now sound slightly different. Can you try explaining what you mean by it more? Maybe I can help out.
If the 12 notes of the octave were on 6 lines and 6 spaces, perhaps with a distinct (dotted, wavey, thick, missing, etc.) line to aid in not getting lost, the situation would be far better. There wouldn't need to be a key signature at all, or any accidentals. Stack as many octaves as needed for the part.
Probably we'll never transition to something sane. We can't even manage to get grand staves with middle C in a unique (shared, central) position, which is what you want when hand distinction isn't required.
We use twelve tones, but most harmony is arranged in seven note scales. Representing those scales easily is important.
I'm at the level where usability matters. Top experts, not that there are enough of them to care about, can handle anything. Beginners will be lost in any case.
I would greatly prefer a chromatic notation. Accidentals ought to be reserved for quarter-tone needs. Chromatic notation gives music the same shape on the page no matter what pitch it is transposed to; this is an extremely valuable property. Sight-transposition would be trivial. Imagine a world in which an ordinary clarinet player could play music for the flute, horn, or bassoon. Sight-transposing, even by other than an octave, would be easy for most players.
I think your ideas here are so interesting! I totally see what you're saying with accidentals being reserved for quarter tones. I studied microtonal music in college and hated the notation systems. They truly feel "bolted on" to standard notation.
Have you developed any sort of concrete "replacement" system? If so, I'd love to see it. This is super cool stuff.
This sacrifices vertical density, but density can be recovered by using finer vertical resolution and using notehead color to clarify position so it's still readable.