Genuine question, who should?
If not that, the only other answer is the parents. Are you as parents willing to give your kids a better childhood at the price of throwing away 10% of your career, with no (monetary) compensation? I suspect, very few. (More will do so with only one parent giving up the years.)
"You can have it all" is a lie. You can't both have a wonderful career, a great marriage, and give your kids all they need from their parents. You can't. What we really need is for people to stop believing that "having it all" is possible, and therefore expecting that someone owes it to them. Instead, people need to prioritize and choose what they want out of the tradeoffs that reality imposes.
I think the brutal/ultra-competitive work culture is uniquely American - Europe seems to do OK with giving working parents generous amounts of time (and money!) to be with their kids; 4 weeks PTO per year is unthinkable in the US, but I'm sure its a multiplier for good parenting.
I do not know if it is possible to change the work-culture when money is king.
But yes, Europe does much better at this than the US. Can the US culture change enough to give what Europe gives? Maybe, but I'm doubtful.
But until it does, my point remains - in the world we actually live in, you can't have it all. You have to choose between various less-than-what-you-want options.
American work culture is only moderately competitive. Many Asian work cultures are much more competitive than the US, where women taking a break to have children will basically end their career (and indeed this is how many women plan their careers), and paternity leave greater than 2-3 days have only started to show up in the past few years. Most of the drive towards more parent-friendly policies actually come from the government, as they try to stem the tide of low birthrates emptying out the countryside.
Literally every single person that has children does this. That covers almost 90% of the population.
1) See having children as a right and benefit to society, then society should shoulder at least some of the "burden" of it. By providing child care, (paid) maternity and paternity leave etc. Many countries already do this.
2) See having children as a privilege and a choice made by individuals knowing there will be sacrifices in time, finances, career etc. In this case, the individual (or couple) deals with the consequences. In some cases, incentives can align such that companies provide paid leave, but at least right now it's not the norm.
Looking at countries that provide paid leave vs those that don't, the ones that do seems to have a healthier society.