And although companies would be able to deduct salary expense to reduce their own tax bill, they still benefit from the tipping scheme. If the worker receives, say, $10 in tips, the company would have to pay them $15-$20 to give them the same after-tax income, since a large portion of the wages would go towards income tax and social security. So, if the worker makes the same take-home pay through tipping rather than wages, the company and the customer both pay less! The real cost is borne by the taxpayer, who has to pay higher taxes elsewhere to make up for the loss.
Even using your logic, your basically admitting its the business owner screwing the general population by creating an incentive structure that encourages tax evasion.
The externality this creates (taxpayers pay more, tax enforcement costs more) which means you are crewing the government out of enough money the customers stop benefiting from the "lower price" since they all have to pay it back in higher taxes to make up the shortfall + increased enforcement costs.
I've actually heard that in many places, the customers actually tip enough that it goes beyond the ability of companies to pay less directly. So the waiters' pay actually does get pushed a lot higher. So high in fact that there's an disparity issue between front staff (waiters) and back staff (chefs), who actually get much worse because they're exposed to pure company pay.