I would hazard a guess that it wouldn't improve.

The kinds of people involved in violence are overwhelmingly poor, young males. This is not a group that cares about laws or cultural norms. They lack the money to pay for sex workers, they don't have cultural hangups about it. They lack the money, education, and human decency to maintain a girlfriend relationship.

Which is to say they're not bad people because they're sexually frustrated. They're sexually frustrated because they're bad people. Which can be a negative feedback cycle.