> (which is probably the most important one to the employer, BTW)

Possibly, but I don't think that is generally true. I eat at a (pretty damn touristy) place two or three times a month and the owner behind the counter is always overjoyed to see me and throws in extra stuff for free all the time. Now, in that particular case it isn't tip motivate, but he absolutely appreciates the regular reliable business. I think that regular reliable business is most important to many small restaurants, which is why you see so many of them offering punch/stamp cards to regulars. If you frequent small locations, it becomes clear pretty quickly that the business owners really do love regulars.

If preferring repeat customers was actually bad for business, the business owner would be well within their rights to forbid tipping at their business and instead pay their staff the proper minimum wage. I suspect this isn't ever actually the case; either repeat business makes up a significant chunk of your business and is more valuable for its reliability, or your business is so touristy that the occasional regular getting better service has no significant impact. Maybe there is some sort of middle-ground between those two, but I suspect it is elusive.

To clarify, the first visit is important for attracting the repeat customers. There's nothing wrong with treating repeat business better, but this naturally accrues as servers learn your name, favourite foods, etc. Tipping potentially complicates this process. For example, what if you tip exactly average? Now do you get better services as a repeat customer?

Finally, in the video linked elsewhere in this thread, Bruce McAdams talks about the effects tipping has on turnover among waitstaff (it increases it). This is probably detrimental to serving repeat business better.

Edit: For that matter, what if you're a repeat customer that tips lower than average? Now the interests of the owner and the waitstaff are at odds. The owner wants you to come back and spend more, but the waitstaff will treat you (relatively) poorly.

It is going to take a lot of concurrent repeat customers to appreciably degrade the service that new customers receive, at which point the value of obtaining new customers is diminished. We don't have to talk in hypotheticals with this though, we need to look no further than how business-minded owners treat repeat customers in real life. Repeat business is preferred business.

Server turnover in practice is unlikely to hurt repeat business unless we are talking about unprecedented amounts of turnover on the period of days or weeks. A churn period of several months or more is unlikely to dramatically harm repeat traffic. Certainly I have never stopped visiting a bar because my preferred bartender left.

Furthermore, presumably if a repeat customer repeatedly gets poor service, then that customer does not care about the quality of service. I get fucking awful service from the coffee shop I usually spend my Saturday mornings in (perhaps because I only take my coffee black, or perhaps because I refuse to tip baristas...), but I don't care because I don't need frequent coffee refills and I mostly like them for their decor.

tl;dr: If tipping really is bad for business, then the business owners would be fighting it. They're not stupid, knowing their customers and maintaining a customer base is their livelihood.