The crazier, more-expensive, and more-difficult the method is, the more improvement it should show; craziness should filter out less-committed parents.

I think there'd be a U-shaped curve. Requiring some degree of effort will select for people who are willing to make good choices. At some point, craziness and expense will swamp out the good effects.

I have an example from food rather than schooling-- vegetarians might be healthier than the average person. Vegans might not be, and it's even less likely for fruitarians. Breathairians certainly won't be healthier than average.