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.
If you want to address violence it would be better to focus on reducing poverty, on education, and on rehabilitation. A lot of violence is drug related, providing a legal market for buying and selling illegal drugs would kill that element crime. Prohibition of drugs seems to be playing out the same that prohibition of alcohol did. Those who do not know their history are doomed to repeat it.
Normalizing prostitution is not likely to move the needle for the reasons I mentioned.
However, honestly "voluntary" prostitution is also too expensive. Which is a big reason for the famed "management level" to exist. Through drugs, physical and psychological abuse they create a much cheaper supply, and only that way the demand can be met.
I'd argue this is precisely the person who should not have access to prostitutes. Their existence, or our inability to adequately police them, is one of the stronger arguments against prostitution.
Unless we’re talking about hi-class hi-paid workers here, which are far from common, this “outlet” has the same (or even lower) voltage than your hand-y discharger, if you get the analogy.
The more realistic result will be you and your kids living amidst endless brothels and their frustrated clients.
But if you are a man with these kinds of problems you have nowhere to go.