The problem with this is how class affects the WILL to be good at school, SAT, college and so on.
If you're high up in the middle class, you have a high-paying job. That means one of three things:
1) medical degree
2) high-end engineer
3) varia (like climbed-up MBAs) (but this is a small group)
Now when it comes to groups in society, the picture looks very different:
Largest groups are non-working people, and workers and tradesmen (from factory workers and construction workers to truck drivers) (total of these groups is like 90% of America)
Both of these groups are famous for disrespecting education, telling anyone who'll listen how college and university degrees are worthless (and for their positions in the world, I'm sure that's true).
And ... surprise ! Their kids mostly don't care about education, and don't score well on SATs (except the ones that figure out they really DO want to in time). Could this be ... because kids believe their parents ?
The "problem" is the entire feedback loop running through society, which mostly is the people itself, not that "rich" people tell their kids to achieve things. You cannot fix this without separating kids from their parents somehow, and you don't want to do that.
The only thing you can do is to prevent the middle class from achieving anything, or anything worthwhile. Which is exactly what is mostly happening in these diversity efforts.
Even that is disregarding the fact that there are already too many college and university graduates to make sure such a degree is definitely worth it. This is a problem akin to "let's make the lowest 50% of the population better off than average".