Again, this is a world based entirely on logic. Logically speaking, a person who won't take care of his own child has put a tremendous financial burden on society. If I molest a child, should I be able to become a school teacher? Why not? Because past behavior predicts future behavior, so the logical thing to do for deadbeats is prevent any further impregnations until they decide they are capable of being responsible.
If anything, my proposal is too compassionate for such a world. Probably better to just remove their testicles and be done with it than give them another chance.