What’s interesting about European Christian churches that were re-purposed pagan temples is that they often retained some thematic elements. Temples to Athena became churches focusing on Mary, etc. In the same way that pagan figures got turned into Christian ones - e.g. the local water goddess of Lourdes, and Tonantzin at the hill of Tepeyac, got turned into Virgin Marys. (And weirdly, in a few cases sites got reused even after intervening centuries of disuse - I recollect visiting the site of a relatively modern church in Sicily whose expansions had uncovered a trove of Demeter-and-child images from an ancient temple on that location, very much like the Madonna-and-child images of the subsequent church. I wondered if Christians hadn’t built a church there originally because they had long dug up such images at the site, mistook them for Mary and Jesus, and saw it as a sign, though.)
It was being rebuilt and expanded when in use, but Gobleki Tepe is one of those sites supposedly built by people who weren’t settled, i.e. it was a place that nomadic people traveled to purely for ritual purposes. I can see how that wouldn’t have the same kind of staying power as a ritual site near a settlement - as soon as people’s lives changed (in that case, they actually started living in fixed villages), ritual migrations would make less sense. There wasn’t enough of a location population to keep it going, even assuming their ritual needs hadn’t also changed with their lifestyle. You also see this with sites where the population centers shifted at some point - without it serving a local community, it fell into disuse, and was either forgotten or just no longer used (and therefore also didn’t get re-used either).