OK, that would work.
Not politically feasible, unfortunately, due to cries of genocide.
All of which gets back to the fact that it is likely none of the options that could get us out of this mess are politically feasible.
Which, unfortunately, means things will have to get a LOT worse, and possibly all the way to catastrophic before necessary actions are possible. And, of course, by that point the earlier range of effective policy options will have diminished greatly.
I don't see a political solution before we reach the point where things are so bad that the underclass are converted into stew.
And middle-class women would be hysterically opposed to it.
One unspoken thing about welfare: no matter how unintelligent a young woman is, there is ONE service she can provide that she can make enough to survive on, if she is moderately attractive. Without welfare, you would have young underclass women willing to do whatever it took to get a middle-class sugar daddy. Middle class women would not tolerate underclass women trying to poach their men.