I had this same thought last year in music theory. My thinking is that it is currently impossible to notate any non-2-divisible subdivision taking partial beats and have that constitute a measure. Since that didn't make any sense, let me explain further:
Outside of a one-bar tempo and meter change, there's no way for me (in popular notation) to say that, for example, I want 13 eighth note triplets in a measure. If the time signature is 4/4, I can fit in 12 eighth note triplets easy, but there's no system in place to add a non-3-divisible number of those triplets to the bar- i.e. I could go up to 15 notes with a bar of 5/4 but I couldn't do 13 or 14.
Techncially, triplets, quintuplets, what have you are just different numerical notes anyways, just notated differently. A whole note equals 1 bar of 4/4, a half note half, quarter is a quarter, etc. So it follows that a third note (currently only recognized as a half note triplet) is a third of a bar, a 12th note is a 12th of a bar (8th note triplet), a 20th note is a 20th (16th note quintuplet). There's no way to say "I want twenty-four 20th notes in this bar" outside of the clunky one-bar tempo & meter change I mentioned before. Todd understands this concept.
It seems to be just an oversight in musical notation. The only conceivable problem with this system is the note appearances- there's already a (frankly somewhat silly) system in place for 1/(2^x) note values, and we don't want more strange noteheads, especially given that those serve a purpose already. I haven't figured out a good system yet, but I think it must be algorithmically based so as to be infinitely expandable (so composers down the line don't run into the same limitations we have come to in the current western system).
I will probably return to this topic if I find a suitable solution. Glad to know that others have considered it!