Two otherwise-identical people of different genders doing the same job are paid almost exactly the same, at least on a population level and with moderate-size or larger companies. To do otherwise is super-dangerous because it is an open-and-shut lawsuit and the information is all discoverable. (Of course individuals may have minor differences due to experience or negotiation at hiring, which generally goes away with tenure - if the company is smart.) You can look at any of the company stats of salaries for like-for-like positions and they're incredibly close to 100%.
This is a fact and is true today. Look at it another way - if a company could get the same work for 77% of what they pay a man, wouldn't they far prefer to hire women? People in companies could be wildly sexist, but they'd fail - that's just too much money left on the table! The 77-cents-on-the-dollar thing is an absolute lie. I'd link to actual articles, but there's too many. It makes me so angry to hear otherwise-intelligent people (like the President!) repeat it - are they that cynical, or do they really not get it? (It's got to be the former - when someone pulled up the WH workforce stats, they were quick to reply that it wasn't fair to compare across titles and experience, which is exactly how the 77c number was fabricated.)
So what's going on? Well, there is undoubtedly a motherhood gap, because mothers generally take time off to be with the new child, which puts them behind their non-childbearing peers of any gender. Some women, of course, don't ever come back, but are still included in the stats. Of those that do, well in some industries it's particularly difficult to take a leave of absence (for any reason) - academia and tech are prominent examples. If I as a man took 6+ months off to go hiking in Asia, I'd be in the same boat.
This isn't that complicated. The question is, what do we want to do about it? Well, it's an unavoidable fact of taking time off. We can incentivize anybody who take time off for any reason by negating the setback with an opposite incentive - this seems highly risky and undesirable. Alternatively, because procreation is a societal good, we can incentivize specifically mothers in this fashion. I trust that women wouldn't just have kids to get this benefit, and who pays for it is an open question, but it still seems like a perverse incentive - and in any case it may not be legal to do this. Regardless, such a change should be an open debate - but trying to fix it by erasing the symptom of the 77c lie would just be sneaking through the back door.
The only alternative I see is to accept that having kids is a life choice like any other, and it has downsides and upsides. The downsides are easier to measure, but maybe not important. I personally don't know many women, including my own very successful mother, whose joy about being a mother is tempered by "but it has reduced my lifetime earning potential by X%". People do things for reasons other than money.
This whole thing smacks of the nasty phase of old-style feminism where women berated mothers for being unenlightened and choosing to have kids. I thought we were past that...