Complementarianism does not influence a home only when the husband follows it, but also when the wife follows it without her husband doing so. When you preach to a woman that she should submit one-sidedly, you are preaching complementarianism into the marriage. If she then submits to abuse and the abuse get worse because she does, complementarian teaching made it worse.
Closely related is the myth that patriarchy/ complementarianism holds men accountable by preaching men should love their wives. Preaching it from a distance is not holding him accountable. To hold someone accountable, you have to punish bad behavior. Teaching a wife to submit to a selfish demand (to reward bad behavior) is the exact opposite of holding a man accountable.