What other way was there to feed a city full of people? Certainly, you could have culture within a hunter-gatherer society, but not civilization. How could hunter-gatherers provide enough food to sustain a city? Unless we redefine civilization by removing cities/urban centers from its definition.
Even the idea of a hard binary between 'agricultural' and 'hunter gatherer' societies is put to the test, with evidence of civilizations that changed both locations and whole modes of culture and caloric intake seasonally.
IIRC there is evidence that Gobekli Tepe was not fully occupied year round, so more of a festival site or wintering ground. Maybe in the later stages it did have a more permanent population, and if so they could have been some of the first people to invent actual farming. This is around the time and place we think Einkorn was first domesticated, and a bunch of people growing it near a festival site to brew booze to supply a bunch of nomads when they come around to party makes a good narrative on how we transitioned from hunters to farmers.
