"less conflict for romantic rivals given the expectations"

This assumes all men would be equally likely to get to have sex with the women. Otherwise, if the whole society has to take care of the children, but only a few men get to procreate, it just means many men working for free (like drones) to support other men's children.

Of course that would be a good scenario for some members of society - the women who can choose to mate only with the most attractive men, and the few lucky men. I doubt it would automatically create a happier society, though.