I agree that the debate over education is crippled by a lack of clear teleological goals that everyone can agree on before discussing. But that's expected in a big discussion.
Most Big Social Issues have this same problem because they are political by nature, not technological or epistemological. Our society hasn't reached consensus on what an 'education' is, just like how it hasn't decided what a good life is (work/life balance debate), what 'freedom' is (drug criminality debate), or what a just war is.
But ESPECIALLY with education, I wouldn't expect a 'defined problem' or a set of agreed upon terms to come about by consensus. Why? Like tax policy, education policy has a very intimate relationship to politics and social classes because it affects everyone closely. The issue of definitions is 'solved' when one group's ideas win by force of influence.
The point you may be missing is that this has already happened. For the wealthy, the system isn't broken at all. The current system of standardization (test scores, bean-counting admissions processes) for everyone with a side of elite tutoring and private schools for themselves isn't failing. It's doing quite well: Pay extra disposable income for Mary to have better 'aptitude' --> secure acceptance into the next stage of life. The wealthy don't want to make the masses dumb, that would be too dangerous and gut their workforce . They'd rather make them predictably average so their children can beat their peers, reliably, with extra financial firepower.
They may not think these details out consciously, but it's the game being played.