At least in the comments, someone goes down this rabbit hole, points out that the generally talked about wage gap (IE the "women earn 83 cents for every dollar men earn" ones) is, at least as being published by BLS/etc an overall one, not an individual one.
IE they are calculating median annual earnings of all women working full time, year round, and then calculating median annual earnings of all men working full time, year round, and seeing what the gap is.
So in fact, even if you pay men and women equally (which 100% agree should be the base case) for the same job, that gap wouldn't get closed because of the effect of job choice, etc.
Equal pay is a necessary but not sufficient condition to close the overall wage gap because of this (in fact, you'd still end up with a wage gap that was quite large, IIRC)