Yes, free market principles still apply, but I’d argue that the proposed scenario allows for a more limited set of free market choices. As you say, I would still have the right to refuse to be a patron of this restaurant and indeed that is a free market choice. However, that would be my only choice. With the current tipping system, I can choose to frequent the restaurant and ask for a specific waiter, I can choose to tip, I can choose to walk out if the service is horrible, etc. I have more free market choices now...so I again ask you why a conservative minded individual would willingly agree to limit their choices?
If more restaurants start advertising no tipping, we will see how “market forces” really play out.
My prediction is that if the no tips restaurants and cafes survive the pressure, then many more will want to escape the tip game and put up their own no-tip signs.
I don’t agree that your choices are limited.
There are many circumstances where your choice gets narrowed down after-the-fact by circumstances to not patronizing a particular business ever again.
It’s not just restaurants. We have the expectation of fair and good business practices wherever we go ... but in reality, as we all know, that is not always the case.
The free market means you are free to take your chances patronizing a business and it may or may not work out well for you. You have various forms of recourse if it doesn’t.
The only other alternative is to have government set the rules for businesses, in this case telling the restaurant they must go back to the traditional tipping system ... which is definitely not free market.