even if everything in there was true, this would still be a systemic problem

Of which no one can responsibly say anything beyond "a nonzero amount of sexism exists". Which it obviously does (and in both directions, of course--even I personally have gotten the short end of the stick more than once for being the only male in my department), there will never be literally zero bigotry, sex-related or otherwise. But there is no evidence that there is enough sexism to create an average difference between the sexes large enough to measure, when all known factors for average earnings differences are taken into account (and there are certainly still more non-sex-related factors that we don't know about and haven't accounted for yet).

This means two things:

1. One can't intellectually honestly say that sexism is a significant barrier to professional women (in the US, at least, all the stuff I've looked into is US-centric), given that the impact of sexism is literally too small to measure.
2. There is no "systemic"/top-down solution to the nonzero amount of sexism that is out there. The best to reasonably expect is that we identify and rectify cases of sexism (along with any other kind of unfair discrimination, of course) on the spot as they're discovered.