But if I'm pinning it to dedicated machines then Kubernetes does not give me anything, but I still have to deal with its tradeoffs and moving parts - which from experience are more likely to bring me down than actual hardware failure.

It’s not like anyone’s recommending you setup k8s just to use Postgres. The advice is that, if you’re already using k8s, the Postgres operator is pretty great, and you should try it instead of using a hosted Postgres offering or having a separate set of dedicated (non-k8s) servers just for Postgres.

I will say that even though the StatefulSet pins the pod to a node, it still has advantages. The StatefulSet can be scaled to N nodes, and if one goes down, failover is automatic. Then you have a choice as an admin to either recover the node, or just delete the pod and let the operator recreate it on some other node. When it gets recreated, it resyncs from the new primary and becomes a replica and you’re back to full health, it’s all pretty easy IMO.

I run PostgreSQL+Patroni on Kubernetes where each instance is a separate StatefulSet pinned to dedicated hosts, with data on local ZFS volumes, provisioned by the OpenEBS controller.

I do this for multiple reasons, one is that I find it easier to use Kubernetes as the backend for Patroni, rather than running/securing/maintaining just another etcd cluster. But I also do it for observability, it's much nicer to be able to pull all the metrics and logs from all the components. Sure, it's possible to set that up without Kubernetes, but why if I can have the logs delivered just one way. Plus, I prefer how self-documenting the whole thing is. No one likes YAML manifests, but they are essentially running documentation that can't get out of sync.