You make excellent points, and I enjoyed reading through. Here's the problem: raising MW to $15 an hour would, indeed, do away with welfare assistance, as the enrollees are then making too much money. In fact, this has been the case in a # of areas where former welfare recipients are now COMPLAINING that the higher MW is now making them inelgible for assistance.
But let's boil it down, shall we? Someone making $15/hour grosses $1200 every 2 weeks ($15 x 80). After taxes, take home pay is likely to be somewhere around $800, so effectively, they are now making $1600 in "take home". In Denver (and comparable cities), rent for a simple 2 bedroom place is extremely high, approximately $1200+ per month. So, NOW they are screaming because they no longer get those welfare benefits, AND the rental market is continues to out price these "low income" types.
The result? How long before poverty rates are jacked up, and folks making $15+ per hour are once again eligible for housing and food stamp assistance, thus being funded once again, by us taxpayers?
Actually, very few government assistance programs simply cut you off if you work. If you make more money, you’d get less money from the government, but your net takehome pay would still be more.
Of course, you pretty much don’t qualify for anything if both parents are married and thus have their incomes added together for means testing. So relying on better wages rather than federal assistance will also have the added benefit of saving the institution of marriage, and all the social stability factors it brings into play.