The economics solution would be to make teachers invest in students (paying cash to teach them!) in exchange for a percentage of future earnings. Taking a cheap student who everyone assumed would be a failure and inspiring and educating him into a successful entrepreneur might then be a better investment than finding a professor's son and providing an adequate education, due to a presumably kpmuch higher valuation of that child.
A problem is that a successful entrepreneur or hedgie is still more likely to come from a middle or upper class background and can easily make 1000x the return of other professions (which are more credential based, and hence a more level playing field for lower class students.). Hence, even at high valuations, investing in motivated, intelligent, well connected students may be the best investment.
Year on year changes would help ensure teachers were compensated fairly, as long as the market provided some kind of feedback to let parents and students evaluate teachers. I assume there is far greater variation among students and among teachers than between the teaching value offered by the same teacher to different students, but that may not be the case.
I don't really think this scheme is workable, but it provides the right economic incentives to everyone.