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.
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.