Solution: pay people a decent wage. Stop externalizing the costs of running a business. If you can't make enough money to keep the business viable, then maybe the law of supply and demand and the free market is trying to tell you something.
That law works on the side of labor too : if competition (more supply of workers vs fewer work slots) for the job is high enough that employees are willing to risk working for a crappy wage plus tips, then employers can still get away with this. As long as regulations permit. I agree that a decent wage is the best path forward.
Why would businesses stop asking for tips if wages rise?
Tipping is a cultural norm in the US that won’t be changed by the price on the menu going up a few bucks. If anything, the relationship is the opposite. You are socially expected to tip better for more expensive meals.