Abusers are at their most dangerous when you try to leave them. They will be even more dangerous if you have to damage their public reputation with the ugly truth to try to escape.

No fault divorce makes it vastly easier to divorce for a lot of reasons and making it unnecessarily hard to leave can foster situations where it becomes abusive because they don't get along that well and can't just up and leave because they want to.

Understood, but in this context of parenting and looming child support, would that not present an equally difficult situation?

That's theory. In reality abused women may choose not to attempt to divorce (or even leave) their abusive husband since they fear retaliation.

How is that relevant? Why would no-fault divorce help that situation?

Fault divorce is more expensive and requires burden of proof.

Abuse isn't always reported, and abusers often manipulate or lie.