I mean, even assuming they spend all the money on better buildings -- if the building is so poorly made that the heat or air conditioning don't work, then that will be distracting, resulting in worse education.

The public school in the town I grew up in had lectures in these shitty trailers that were supposed to be temporary (spoiler: they became permanent). They couldn't afford to hire enough teachers to do small classes, but if they had the money for that, there wouldn't be enough rooms put them in.