Is there a legal anchor to this? I was under the impression that "minimum wage" is a salary they must be paid or otherwise it is illegal to employ someone (at least this is how the minimum wage works in France)
So if you earn $5/hr and minimum wage is $10/hr, you are guaranteed $10/hr but if you are receiving tips then the remaining $5 comes from your tips. If you do not, the remaining $5 comes from your employer.
However, a lot of tipped workers earn well over the minimum wage when you include tips. So if the proposal is: "let's get rid of tips and then you can get minimum wage," that's obviously not desirable. What would be more palatable is getting rid of tips and raising the minimum wage closer to what they earn with tips, which is really more a problem with the abysmal minimum wage than it is with tipping per se.
We have a minimum wage of 10 USD/hour in France (net, after the zillion of taxes) but the actual minimum is based on a collective bargain that exists in some families of employment (including waiters). The average net salary for a waiter is 1700 USD/month (this includes retirement, social security, unemployment etc.) - not sure how this compares with the US (if there is a way to compare at all, taken how vastly different the systems are)