I was chatting with a friend of mine who happens to be a judge... He said that the vast, vast majority of custody arrangements are now joint custody, not the mother retaining sole custody. Even in cases of domestic abuse, the father often maintains equal custody or close to it. He's also seeing an upswing in fathers maintaining custody with the mother having visitation. Maybe the sample you're seeing, Francesca, is a bit skewed.
I used to know a guy who had two kids by two different women (neither intentional) and paid child support - a grand total of $100 a month per kid. Poor boy. Basically, if the guy can cry poor he doesn't wind up paying that much and the brunt of supporting the child (he didn't want custody, actually was offered joint custody in both cases) fell to the women.
Knowing that anecdote does not equal data, I don't think we can equate him with the majority of non-custodial fathers or fathers sharing joint custody. We do know that such people exist, as does the stereotypical divorcee out to ruin her ex financially. It doesn't mean that it's the norm.