What evidence is there that this is true? The truth of it seems to depend entirely on what the hypothetical minimum wage for those workers is set at.
.[...]tipping is a form of price-partitioning that reduces perceptions of expensiveness even when it does not affect the actual total costs of eating out, so replacing tipping with service inclusive pricing may decrease consumers’ perceptions of value."
Some pretty big names in the business have tried banning tips in the past few years, and it's been largely unsuccessful -- in some cases disastrous -- and the restaurants have almost all had to return to tipping to save their businesses. A few brave souls persist, but it's safe to say the anti-tipping movement in the U.S. has kind of petered out for now [2].
I suspect that if an entire city were to ban tipping, it would be much more successful since individual restaurants would not be at a comparative disadvantage due to whacky price perception.
I personally hate trying to figure out tips. I cope by just adding 20% by default in every case, unless the service is truly awful.
1 - https://static.secure.website/wscfus/5261551/7004898/ijhm-ti...
2 - https://www.newyorker.com/culture/annals-of-gastronomy/the-l...
That's why they're fine with their salary being less than federal minimum.