> customers are uncomfortable and sometimes try to tip anyway

This is almost certainly largely because of another of the incredibly frustrating aspects of tipping: it's entirely informal, with no way to tell what's expected of customers. The etiquette around it can be extremely confusing on both sides, too—I've heard stories of workers who are strictly forbidden from acknowledging tips to customers, so that if you asked, they would have to say "no, you don't need to tip", even though they're still considered tipped workers legally.

So unless there's explicit statements from the establishment of "we do not accept tips for our workers, because we make sure their wages are high enough not to need that", you can't take "you don't need to tip" at face value. Hell, even then you can't; I wouldn't be remotely surprised to see unscrupulous business owners put that even when they do not, in fact, pay their workers well, especially in areas near where other places say it truthfully.