In Britain, bills usually say "Service charge" or "Service is included" [1]
But I think these are exceptions, and I wouldn't expect it in general -- just like it doesn't say "Service included" when I buy a buy shoes in France or Britain, even though the staff usually have to fetch them from the stock room.
I was recently in a restaurant that had exactly that. There was a fine print note at the bottom of the menu explaining that because a state law prevented servers from splitting tips with the kitchen staff, a 3% surcharge would be added to the check so that non-tipped staff could "earn a living wage".
https://www.squidlipsgrill.com/wp-content/uploads/2022/01/Sq...
That's why I started this by saying I'd have an issue with someone who kept not tipping after being informed about the issue.
But I'd be hard pressed to come up with a reason that "customer -> staff" is objectively better or worse than "customer -> owner -> staff".
Same money, gets to the same place.
It does more than confuse tourists, it locks every restaurant into the system whether the owners wish it or not. That’s why I think the “we underpay” with its pejorative tinge is inappropriate.
There should be a note on American menus that says "We underpay our staff, so 15-20% tipping is expected." And European menus should read "We compensate our staff sufficiently, so tipping is not expected."
In reality, both of these are never written out, and everyone is expected to learn them culturally. Which ultimately leaves tourists in an awkward spot.