If there are countless studies showing this why does nobody ever seem to cite them and instead fall back on just counting men vs. women or raw salary data? The studies I have seen which take into account the difference in the choice of jobs and the years of experience show far smaller differences in salary.

For example,  this survey (http://www.payscale.com/gender-lifetime-earnings-gap) shows that the gap opens up around age 30 which is when educated women typically start to have families. If this is the cause of the pay gap then you can create all the quotas you like but it will not address the problem. Indeed, if this is the cause it is arguable whether it is a problem or a reasonable consequence of the difference in the choices which men and women tend to make.