> Waiters also explicitly aren't allowed to be paid less. They must make at LEAST minimum wage. If they don't make minimum after tips, their hourly rate is raised each paycheck to equal minimum wage.

That means they are allowed to be paid less than minimum wage. Wage is paid by the employer, not the employer's customer. If the employer can deduct the tips from the minimum wage, that explicitly means that they are allowed to pay tipped workers less and that tipping does not provide any additional income but instead only shifts the responsibility of paying people for their work to the customer. Tips are are nothing but gifts to the employer.

> and it's an easy way to show appreciation.

If something is socially expected simply as part of protocol and people only do it out of the social pressure not to deviate from the norm and be seen as assholes, then that is not appreciation.