But aren't there a large set of interdependent factors?
Like, if everyone knows that the wait staff gets paid $15/hour then wouldn't there be less pressure to tip, say, 20% on meals? If all wait staff received at least $40/hour then I'm sure that most people simply wouldn't tip.
And how would this change, to include tips as part of wages, help the "near-poverty cooks and dishwashers"? Are the businesses on the knife-edge of solvency that they simply can't afford to pay the back-end staff more? It seems more likely that the savings will go to the restaurant owners?
You mentioned socialized health care. Doesn't that also affect the labor costs? That is, the US government already pays more per capital on health care than just about every other country - then there are private health care plans on top of that blowing the costs sky-high. By switching to socialized health care, it should lower the overall healthcare costs, so make it cheaper to employ people ... unless of course the restaurants currently don't provide reasonable healthcare coverage to their employees.