That's the main reason why men should not get married and have kids in the USA.
The proponent of exclusive custodial control must prove the other parent's unfitness for custody. This is easy, if say, the other parent is a convict or a drug dealer. It's not so easy for suburbanites or rich folk. While the bar is lower than criminal guilt, it's not much lower -- proof must be by "clear and convincing evidence", which is significantly higher than the usual civil burden of "more likely than not".
Indeed, in over 90% of the cases I worked on, the exclusive custody proponent lost. The myth about mothers always getting the children isn't just a myth, it's blatantly untrue. Where exclusive custody is awarded, the father is just as likely to get custody of the children (usually b/c the mother does not have a job and is unable or unwilling to find one).
Kid, I worked in Cleveland. If there's any city where mothers should be "stealing" the kids from their fathers, its going to be a city where more than a 1/3rd of the male population doesn't have a job.
There are no such sites for women. That should tell you something.
Also look up alien abduction, underpants gnomes, and other urban legends.
I don't claim that courts in the past favored mothers, but in the present, there is no gender bias under the law.
When divorce happens, that's when you see what people are really made of. Some women will take custody just to hurt dad.
Anyway, I hope you're right about the lessening of gender bias. I'd love to see data. No idea where I'd find such data though.