Sorry, I have to disagree. I had a no-fault divorce with my first wife, and we have a kid together. Just because the woman and I don't get along, doesn't mean that I'm not entitled to visitation/custody of the boy. I pay support like a good parent should.
If the spouse is requesting a divorce because of reasons such as spousal abuse, affairs, and other legitimate reasons for getting a divorce should clearly have the ability to fight for and get the kids.
But when a spouse decides to just cut and run to head for greener pastures, the spouse should not be able to pack the kids along.