It also doesn't make good business sense. The private sector is competitive, if you're making business decisions based on things that aren't relevant to the bottom-line then you're going to be out-competed by those who are more practical. So biases which don't make business sense are going to be damped down in the long run due to the necessities of competition, and this is a fractal thing, competition works at the personal, department, inter-department and inter-business levels, and no less in private business than in public institutions.
Wage gap for the same job doesn't make sense either. If women will do the "same" job for 77 cents whereas you need to pay men $1.00 for the same level of performance, then any sensible business would set a single pay rate of e.g. 80 cents and have about 90% women doing the job. The men would just be cut out of that job market completely, since they are below par in cost/performance. Any business which did pay more so that they could hire men for that role would either go out of business, or attract more highly-skilled women. e.g. if you did pay the full dollar, you could either hire an average male or a 20% above-average female, so even if you paid more to attract men, you'd still find that the women coming to you were exceeding the performance level of the men. The theory of women paid significantly less for the exact same work doesn't make much common sense.
Basically it doesn't make a whole lot of sense for their to be pervasive bias against skilled women, because that merely gives your competitors access to a more cost-effective skill pool, and loses you money. it's like saying you don't hire people call Steve, then wondering why Steve Jobs and Steve Wozniak are working for your competition. If one company isn't hiring high-skilled women it's just an opening for other companies to get ahead.