It's not clear what you're asking for exactly, but the solution is obvious: give whatever it is that you want to provide to EVERYONE, regardless of their gender, and whether or not they actually have children. Special treatment for everyone.
For example, in most top universities, they give roughly the same leave to new fathers as new mothers. New mothers use this time to care for their baby, but many new fathers use this time as an extended sabbatical/research leave. Their wives take care of the baby for the most part, and they work on their next book.
Then when it comes time for tenure review, the men who did this have accomplished more than they would have if they hadn't had kids (and more than some faculty who are mothers, who spent their leave with their baby).
So when everyone gets the same treatment, that doesn't necessarily reduce or eliminate disparities — and in some cases it can exacerbate them.
Let young boys play with dolls. Celebrate fathers who parent young kids in movies and TV shows.
If the husband and wife agree that they want to use their combined paternity/maternity in a given way, who are you or I to tell them that they can't? The wife could just as well force the husband to take care of the child and work on her own next book. Or the pair could stagger their leaves so that they spend equal time taking care of the baby.
I was under the impression people had kids to build a family together, not to compete with their partners for achievements. I don't think at all the situation you described is bad in any way. In fact, it would be a huge step forward.
You know what is better then a new father stressed at work, absent from home, worried his career is not growing fast enough? A new father excited about the future, doing something that is quite easily interrupted to help with the newborn and building a future for the family.
I do agree giving everyone the same things would be the best, but it is easier said than done. Easier for large corporations to support larger universal parental leaven than to for startups to do the same.
I wasn't indicating that the spouses were in any way competing with each other. I was pointing out the inequity that results among professors who are fathers and their colleagues who are mothers. The seemingly generous and 'equal' policy of giving the same leave to mothers and fathers has the result of disadvantaging professors who are mothers, on balance.
(I should note that not all male professors spend their leave in this way, but enough of them do it is a problem.)
Also, I never suggested anything that would violate Title VII. At most law firms (including the one I worked at for many years), a parent who birthed a child received much more leave than the other parent.
How do they even focus with a crying baby in the next room? And how do their marriages survive such an abdication of responsiblity?
As for their marriages, it's not necessarily an inappropriate division of labor; one partners is earning money and the other is caring for a child. The potential unfairness is that it tends to result in men getting more work done, and appearing to be either more productive or more intelligent than women whom they work with.
He did spend some time caring for his new children but if his case is representative then, for a male, having a child is like getting extra paid time off which is not fair to people who may not use paternity leave.
To the VC partner's credit, he stopped the meeting when he saw the bracelet and I explained what it was (and re-scheduled the meeting for a couple weeks later, so it wasn't a blow-off; I still didn't get funded, but it left a positive impression).