While agreeing with you entirely that legitimaacy must be re-emphasized, I still say you have failed to show how your solution (abolishing financial liability for unwed fathers) honors the natural right of every child to his father's support and provision.
If only married fathers have this responsibility, while unmarried fathers can (in your scheme) get off scot-free, you further decrease the likelihood that men will seek marriage.
Women (plural) in general need to re-assert the sexual rule: no matrimony, no sex. OK. But in each and every case where a man and a woman have produced a child by their sexual union, both the man and the woman must be called to responsibility. Otherwise you have only the woman being treated as a responsible adult, and the man being treated as somthing less than an adult: either a mental defective, a rutting animal, or a perpetual lad.
You seem to that illegitimacy is a good thing and want more of it by rewarding women for making illegitimate babies. Why would they even bother to get married? Collecting half a dozen support checks and sleeping with whoever they feel like is a much better deal than marriage.
I think illegitimacy is a bad thing, and that if you make it unpleasant and financially devastating enough there won't be any illegitimate children born to be deprived of their illegitimate father's "support and provision."
Problem solved.