I'm not sure what you're asking, Bobert, but the implication doesn't make much sense. You shouldn't be able to have it both ways. If conservative thinkers are the ones who opposed welfare in the first place, it is not likely that they are the architects of the program as implemented.

If there were some short-sighted rules built into the implementation of the welfare program (like making sure there is no man present), why would you conclude that that is a "conservative" idea? That doesn't make any sense.

Why don't you tell me why the architects of the program decided it would be for women and their children only.

If I were to guess, I would say it was an initial attempt to stop the practice of men maintaining a stable of "welfare bitches", wherein a man enslaves a number of women in order to get their government check to use on his drug habit.