Eh. I can see it working.

Humans are social creatures. We like to feel useful and connect with others. In a world with a replicator in every home, dining out is much more about the social experience than the food. Restaurants would be about experience, community, and shared interests. People would volunteer to staff them for the same reason they do any form of volunteer work: they enjoy the sense of purpose, skill-sharing, and camaraderie that comes with it. Plus, with replicators making preparation and cleanup trivial, there’s a lot less labor associated with food service.

Lastly, consider that post-scarcity dining establishments that would have no tolerance for rude customers. If someone went full Karen on a volunteer, they’d be banned in a hot second. The social dynamics of such an arrangement would entirely favor the staff: if there are no “paying customers” then there’s no entitlement to go with it.

For all these reasons, it’s not that hard for me to envision a set of social incentives that would keep restaurants alive.