My opinion is that men with means will get what they want without needing society to approve in any concrete way about their activities, so anyone able and intending to keep a woman on the side is probably already doing so. And my idea of a 'concubine' is very much of that of a 'side woman'. Even if society approved of concubinage there are enough broken families producing enough drug addicted runaways that no-one has the time, money or inclination to take responsibility for, except the pimps who exploit them. Ah... and they aren't looking for a nice guy...
The addition of a social niche that could be an alternative (I don't believe) will significantly reduce the impact that (A) Women crave male attention, money, and vanity (B) Men are eager to exploit women.
Reducing this problem to a simple economic one will probably be a mistake, because the principle problem with all economic systems is not that they couldn't work, but that the economies are entirely populated with BAD PEOPLE for whom no system can function without victimization. Some systems merely deal more realistically with how bad people really are.
In this case, my opinion of humanity being what it is, I think instating concubinage.. or legalizing polygamy... will not over much reduce prostitution.
Maybe if society became OVERWHELMINGLY patriarchal to an improbable degree, and experienced a revival of epic proportions: Where women did not and could not easily leave their husbands, where daughters stayed in their father's house until marriage, where the penalty for rape was marriage, and where even non Christians were raised to conform to christian morals. And then yes, men being allowed to keep multiple women as they are able to provide.
Maybe that might put a dent that would be noticeable in prostitution.