You either haven’t read as much as you claim or you are dozing off during the reading then. It’s an unexamined ASSUMPTION on your part that domestic violence has nothing to do with unhealthy sexual behaviors - and an incorrect one.
When a man lives as if his sexual actions are irrelevant to the other aspects of his moral character, he becomes more and more blind to the decay of his overall moral character. The man who has sexual relations whenever and with whomever he feels like necessarily grows to see others as objects that are useful for his own gratification and when said objects are inconvenient or have needs of their own he easily becomes angry and prone to violence. When a man realizes the power of human sexuality and respects it by making life choices in accordance with the purpose of human sexuality in the first place, sexual intimacy is less prone to becoming an occasion of gratification and more likely to be one of self-gift.
I’m no social science observer, but I’d expect that if you looked into it, you’d find that men who have never had a sexual partner other than their own wives have an almost non-existent rate of domestic violence while men with a large number of sexual partners have sky high rates of domestic violence.
In other words, sin begets more sin. Always has, always will. You’ll always fail at trying to reduce the sort of sins YOU find loathsome if you simultaneously attempt to rationalize the sins you personally don’t object terribly too (or perhaps are personally tempted towards). The church HAS TO argue today with modern society when society attempts to relabel sins as virtues. Nobody is arguing that domestic violence is good, so there isn’t anything to argue about. But domestic violence arises largely out of objectification and lack of respect for women and you’ll never reduce it until men and required to respect the innate dignity of woman. That will never happen as long as society continues to treat women as self-propelled pleasure devices. That’s not about “feeling morally superior” it’s about actually doing something effective in the world instead of just hand-wringing.