(This is simplified and generalized)

In the short term it would be worse for workers. Their employers are only required to make up the difference in pay to the non-tipped minimum wage (the normal minimum wage). With tips most servers are making above minimum wage (depending on the restaurant some servers are making quite a bit more than minimum wage; it can be a viable career for some). If a server had been making more than (non-tipped) minimum wage, and everyone stopped tipping, they would probably lose money since their employers are not required to make up the difference to what they had been earning with tips. Since the federal minimum wage is not a livable wage for most of the population, this would be very bad for the servers.

Longer-term it could make a difference, since those servers would likely start leaving their jobs for better paying jobs elsewhere and the restaurants would have to raise their base pay to compete or risk closing. To some extent we’re already seeing this in some industries. I’ve noticed most of the fast food restaurants (non-tipped) are advertising starting pay close to double the federal minimum wage. If the crisis became large enough Congress might be forced to finally raise the minimum wage.

Making employees rely on tips instead of paying them a fair wage is a bad system. I’m not sure how to end it in a way that doesn’t hurt the employees, though, short of congressional action.