> I've heard that much (not all) of the aggregate gap (i.e., on the national level) goes away after controlling for those variables.

The question you may ask here however is: Does it matter? I mean I agree that it matters from "getting the facts straight", but maybe not necessarily from the conclusions.

If the pay gap is due to less experience, less education etc., then you're seeing effects of earlier discrimination in society. Shouldn't it be the responsibility of the society to compensate for that?