The entire point of tips is that they are the workers', 100%. It's also a variable cost based on the willingness to pay, so it creates a form of price discrimination, where those willing to spend more, spend more, those wanting to spend less, spend less.

Those two factors lead to the inescapable conclusion that tipped staff make more money. Price discrimination captures surplus value that simply is not available to schemes that don't use price discrimination, and any new price discrimination scheme would almost certainly benefit the employer at least in addition to the employees, if not be entirely captured by the owners.

Combined with the, let's say "extra judicial tax incentives", non-tipping restaurants simply cannot compete with tipping-norm restaurants for service staff. In an environment where tipping exists everywhere else, you then get an adverse selection pressure for shitty waitstaff, because if they were competent they would be working somewhere that competency would earn them tips. Which piles on top of the dealignment of incentives to create substantially lower quality service.