I really did. Kansas State House ten years ago. I lost, alas, have relocated to another state and doubt I'll ever run for office again.
I honestly don't know why someone hasn't already completely re-thought the semester system at the high school level. I can't imagine re-doing it at the college level, but in high school it seems to me that it would be highly feasible and could work. However, I have never taught school at any level, so there may be some very important things I'm overlooking.
It would require more record keeping, that's for sure. And scheduling classes would be more difficult, especially things that must be taught in sequence, such as math, foreign languages, and some sciences. You'd need to offer the beginning of those things more than once a year, so that a student who didn't flunk the very first sequence in algebra didn't have to wait an entire year to start again. Same with the foreign languages. I do think the sciences could be looked at and after the very first six week intro in biology, chemistry, or physics, the rest could perhaps be taught as topics in those sciences. Again, I've never taught them and so I may well be wrong here.