Folks defending the system claim that most men don't even ask for custody, and that this explains a large part of this. What do you say to that?

It simply reflects the results they expect to get if they fight it out. Lawsuit settlements (and that's pretty much what this is in the family law context) tend to reflect the results that would be expected if the case was tried with smaller monetary settlements to account for time and money saved by forgoing trial. Cases only get tried if both parties think they can gain more at trial than what the other party is offering to settle for.

It's a little different in family law because they they're fighting over a finite resource (custody percentage) and the courts aren't honest brokers, but a lot of the same logic applies. The rule in family court is that the woman wins unless the man walks on water and has a shit ton of luck, so the settlements (custody "agreements") reflect that. Could the woman offer some custody to avoid a fight? Yeah, but they're out to completely and utter destroy their husbands for cash and prizes, and since the court is going to hand the bitch what she wants on silver platter anyway after a show trial she doesn't really have much incentive to do so. Besides, if the guy offs himself she gets all of the assets and custody instead of just the lions share.