It’s the large earners who insist that the woman stay home with the kids who then try to take the kids away if there is a divorce, let’s say when he gets his secretary pregnant and wants to move on. There are special divorce lawyers who only handle contested divorces from professional men who try to destroy the mother of their children pursuant to divorce. Men who can well afford the $20K. I know of women who have paid up to $80K just to keep partial custody of their only child from men like this.
2) The type of person you are talking (post graduate degree, high income with kids) about are also the least likely to get divorced by a wide margin. And even in the extremely unlikely scenario they win custody of the kids, the man would still be paying alimony out the ass for at least 10 years or more (I live in a lifetime alimony state) plus give up half the assets
3) Women initiate divorce 75% of the time.
Another thing I’ve noticed is the type of women in those situations you are talking about are usually lying about a lot of things. About the only time the man can actually get custody when both parties want custody - no matter how much the man spends - is if the wife has severe depression issues, has substance abuse issues, is physically abusive, is sleeping around or more than one of those. In most states with a stay at home mom, the guy is paying for both his and her lawyer as well.