there is nothing ambiguous at all about the current notation scheme(for 3x3 at least). it is extremely straightforward and i understood it before i finished reading the passage about it back when i first learned
here is why your suggestions for new notation will not work:
Color notation: as it has been pointed out already, you would have to learn many times the number of algorithms based on how you hold the cube. and even more obviously, the varying color schemes. what abut people who have cubes with pink or black or purple stickers? what about megaminx, where there are 3 shades of blue and two shades of green? since so many cubes have different colors, all algorithms would be personalized for each cube, which is the worst way to "reach the huddled masses" as you say.side notation is best because by definition, every single cube has a right, left, front, back, up, and down face
why prime notation is best for 3x3: it is easiest to handwrite. plain and simple. a 1 would not catch on, because my 1 looks identical to my lowercase L(i imagine many others would have the same problem.) also, as trivial as this may sound, it takes longer to write a 1 legibly. if you don't believe me time yourself writing ' ' ' ' ' ' ' ' ' ' compared to 1111111111(make sure they don't look like lower case "L"s)
this is actually why other notations (*, #, ~, i) have also not caught on.
and besides, why does it matter if the symbol is arbitrary? every punctuation mark and every letter in every language is arbitrary (except for chinese characters, egyptian pictographs, etc.) and nobody questions them. in fact, changing from prime notation would probably be just as difficult as changing the question mark. it would take the collective effort of the thousands of people using prime notation to alter it. and it is frankly not worth it just to satisfy the only person i have ever heard of that has a problem with the current notation system(you).