@jca2 The way you expressed the question, I can only answer for myself in terms of the appeal of other coffee shops that make better coffee than Starbucks does. Those require finding and testing out.
A really good drink is an experience, and not one that can be had easily in other ways. Yes I have become good enough to make such drinks at home, and I do practically every day, but… at home.
When outside enjoying a road trip, it’s nice to take a break and enjoy a pleasant experience, which such a drink can provide…
… especially if the location is nice and hospitable, which provides the other half of the reason. Starbucks (and sometimes even more so, a cool non-corporate coffee-shop) provides a usually nice comfortable hospitable hang-out where you’re welcome to sit, potentially for hours with wifi, a nice bathroom, and other treats. The atmosphere is not only nice and relaxing, but often suitable for study, doing creative work or programming, reading, and/or can be a daily hangout where you meet and know people, possibly arrange dates, business meetings, play games, etc etc.
Other people use them in other ways, for convenient stops when driving, or to get drinks with lids, handles, carriers, etc. When on the go, various refreshments compete with each other, and Starbucks is a known quantity (or similar places may offer a high chance of being similarly good or better), and while you could get a known quantity from a cheaper place, at least for my tastes, those are often known or extremely likely to be much much worse.
Oh and if you want cheaper coffee, you can get drip coffee at Starbucks for something like $2, pile it with cream and sugar if you want, and you can get a warmed flavored bagel for much less than the other overpriced junk too.