They won't take it in equal amounts unless you literally force them to. Most advanced nations already
have gender-neutral parental leave. Even in Sweden, where they have massive carrot-and-stick incentives to try and get dad's staying home, mothers account for 75+% of all parental leave taken.
In fact, there's a strong correlation between generous family leave packages and a rising wage gap. Countries with a "screw you" attitude to new mothers actually tend to have the lowest wage gaps. Because women literally can't afford to take time off in those countries, so they foist babby off to grandma and keep working! This makes that woman a more cost-effective employee for the employer, and that makes all women more cost-effective to hire on average, driving up wages.
In fact, look at Sweden in this
PDF. Note that Sweden tops the OECD for wage gap, and this is "despite" their massive parental leave scheme that's tax-payer funded (which should mean it doesn't affect company bottom-lines). Note that the "no-children" women in Sweden have a
particularly high wage gap, almost twice what similar women in the USA face. The paid parental scheme therefore incentives mothers, but at a cost to single women more so than men.
So what's the mechanism here? There's the fact that women taking time off costs their employer's
money. Through lost productivity, replacement labor, and/or direct payments. That means the total costs-per-employee is higher for a woman who takes time off to have a kid, compared to other workers. The company can be
non-discriminatory, and just eat the costs but act like they didn't. The problem is that those costs have to be paid for somewhere: they drive up costs in that company, which drives up prices, drives down demand, and means less pay rises. A company that's 2/3rds women is going to be offsetting a lot more of those childcare/parental-leave costs than a company that's only 1/3rd women, which would cause a pay gap between both companies, all else being equal. So you can see a way in which companies trying to be non-discriminatory to parents-vs-nonparents can actually feed the wage gap.
Parental leave is like free Ferraris for men. If the law said every man had to be offered a free Ferrari by his employer, it might be
fucking great for dudes who get their free Ferrari, but it also means it now costs a lot more to hire men. So we pass a law that says you can't discriminate against men - especially not asking them about their views on Ferraris - you need to pretend they're not likely to ask for a free Ferrari, and you pay them the same as you pay any woman (on non-Ferrari driving man) who works in the same company. What do you think would happen to men's wages in that scenario? Imagine if you were a man, the only guy in the company who didn't
want the free Ferrari, now your wages are cut along with everyone else to pay for the Ferraris. Forcing employers to pay "extra" for one gender to "help them out" actually means lower wages down the line for any industry that employs them.
In other words, we have different things we'd like to incentivize, that are
all good for women, and we might be deluding ourselves that they can all be had at the same time. You can find articles by middle-age feminists who say the "you can have it all" feminist mantra that arose in the 1980s is bullshit, that not only is unachievable, but it dips into the quality of each of the things you
do have, while also making women feel like they failed because they couldn't juggle all the things they're meant to be. Fashion model + mother + career women + concerned citizen. Whereas if a guy nails just one bit of his life we usually applaud. Yeah, you can "have it all" as long as you're happy for each component to be crap, or a mere hollow facade.