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.
It is an un-called-for inference on your part to say that I think illegitimacy is a good thing, since I have already made it clear that I oppose illegitimacy, and in fact I would argue strongly that only matrimony ---ONLY matrimony ---justifies sexual intercourse, for anybody. (Can I assume you'd agree?)
But the probem is more than illegitimacy. For decades, the USA has had, for its native-born (non-immigrant) population, a negative fertility rate, less than replacement. Of those American infants who, despite contraception, sterilization, and abortion, manage to be born alive, 40% are born out of wedlock.
If you simply make live childbearing a total loss for unmarried women, you will guarantee a huge upsurge in abortion. Not only is this morally repugnant in itself, it would also have the effect of causing a dramatic population collapse in the USA, bankrupting our social institutions (beginning with Social Security and Medicare, which are already teetering on the edge -- but eventually all of our institutions), and gaining a great victory for the establishment of the Islamic Caliphate of America.
Dare I ask why you are in favor of mass abortion, depopulation, and the triumph of th Caliphate?
No, I won't assume that those are your intentions: but I must repeat that those would be your consequences.
The underlying problem is the failure of family-formtion and dying-off of durable human bonds. The solution can only be the re-building of bonds: between men and women (marriage), between women and children (through honoring and rewarding a fully responsible mother/child relationship), and between men and their dependent children, (through a re-assertion of the honors and obligations of husbandry/fatherhood.)
It's a tall order.
It can't be accomplished by severing the ties between children and their natural parents, either through forced adoption (as Holdren wants), or by authorizing men to abandon their offspring without even a financial liability (as you have recommended.)