The fact that this isn't common is mind-boggling to me. If a student can prove that they know the subject well enough that them sitting in that class would be

The fact that this isn't common is mind-boggling to me. If a student can prove that they know the subject well enough that them sitting in that class would be a waste, then why does anyone think it's a good idea to make them continue sitting in that class? My first guess is "there are some pushy parents who will want their kid to be in a higher class even when their kid isn't qualified for it". The answer to this is, have a rigorous test and a high standard for skipping a class. My second guess is "teachers have a general stance of not wanting to make any 'concessions' to parents, otherwise that will attract more pushy parents". (I did once have a math teacher who said "If I let you ... then I'd have 100 parents wanting the same for their kids.") So... keeping a strong negotiating position for the teachers is more important than doing right by individual students. I think the answer is that, ultimately, the people making decisions about children's education don't have strong incentives to make it go well. If the kid sits in class bored but not causing trouble, that doesn't create a problem for the teacher or the principal; if the kid is enthusiastically learning in the next-level class, that might be nice for that teacher, but on average likely won't make a huge difference—and actually the teacher whose class the kid came from will get a replacement student who might need help, so that teacher may be genuinely disincentivized to recommend the kid's advancement, even aside from the "negotiating position" aspect.