So Kay Hymowitz asserts.

the biggest reason we probably won’t see a lot more college-educated women walking down the aisle with their plumber is one we don’t like to say out loud: they want to have smart kids. Educated men and women are drawn to spouses they think will help them produce the children likely to thrive in the contemporary knowledge-based economy. That means high IQ, ambitious, and organized kids who will do their homework and take a lot of AP courses.

As she points out, this serves to increase inequality. My guess is that it is a far more important driver of inequality than any government policy or lack thereof.