I don't see how raising the "minimum wage" affects things in restaurants. But IF for some reason the federal government has indeed taken over the restaurant industry and can actually force owners to pay waitresses $15 an hour, then that is the very moment that tipping becomes an obsolete and outmoded practice, since its economic justification would have disappeared. (But you can still be free to give a free gift to whomever you wish.)
Cities and State have taken to their own minimum wage laws separate from the Federal Minimum Wage. That applies to both the dollar wage and what classes of workers it applies to. In San Diego, Seattle, San Fransisco, etc. they have not only raised the minimum wage above the Federal $7.25 but apply it to restaurant servers.
Part of their rationale is that when the restaurant is slow, through no fault of the servers, they have to be there but are earning no tips. Requiring the minimum wage at least means they don’t lose money going to work after figuring transportation costs. $2/hr for a 6 hour waitress shift might not even cover gas there and back. That’s got to be fairly discouraging to a server. Requiring $10/hr or $15/hr seems excessive, though.
When I was waitressing in the late ‘60s, my pay was $.90/hour in Binghamton, NY. Tips paid for my college.
The discussion revolves around STATE mandated minimum wage laws, which apply to waiters and waitresses if the relevant legislature says so.