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.
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.