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There's a difference between "stopping something" and "discouraging it."
This is a common argument from secularists when they realize there's not much of an ethical argument to the removal of religious moors, that many of the moral values they hold dear have religious roots. "Well you can't stop it completely!" You can't stop blacks from stealing bikes completely either. You can discourage it, though, put fines on it, put social shame on it, and maybe that's enough of a motivation for some people to not steal fucking bikes.
You're also completely wrong, because hookup culture is probably the most fragile, modern institution there is, and it's so fucking easy to break because women are much more averse to breaking rules than men (See: How many people are squealing over abortion rights in the states right now. Almost none of these people are willing to get the coat hanger abortion they love the bring up.) You get rid of professional abortion, and then you stop fucking paying women for having a baby. Things will get real fucking puritan real fucking quickly.