I'd predict that restaurants would start charging 15% more on all meals. Waiters would still get about the same amount. The only difference is that the money would be taken equally from generous and stingy people instead of coming disproportionately from the generous, and given equally to good and bad waiters instead of going disproportionately to the good.

My impression is that this is true, that the US has "good" waiters, the kind that are get big tips, but that this has nothing to do with restaurant service. That varies geographically, but is uncorrelated with tipping and has a similar range in the US and Europe. I recommend the discussions on Marginal Revolution