Every server would quit and get a different job because no restaurant is going to match what they were making in tips, and it's not worth the hassle to serve for what the restaurant could afford. Service quality would regress to the minimum, because there's no incentive to provide prompt, high quality, friendly service.
Anyone who's never waited tables vastly underestimates how much the tip incentive effects your server checking on you frequently, answering your questions and making recommendations, getting your food out quickly and ensuring everything is satisfactory, refilling your beverage frequently, bringing your check promptly, and doing it all diplomatically even when you're being an asshole.
Frankly, I think American service expectations are a bit high, but if you're used to it then all that would stop very shortly after the customers stop tipping. Think of the performance of every other minimum-or-near-minimum wage hourly worker. That's your server. Anyone with the professionalism to maintain that kind of service will move on to Sales or something.