If kubernetes cannot run a database then what good is it? (And I suppose the same issues pop up for things like a persistent queue or a full text indexer.)
The end goal of Kubernetes is to able to create and recreate environments and scale them up and down at will all based a declarative configuration. But if you take databases out of it; then you are not really achieving that goal and just left with the flipside of kubernetes: a really complex setup and a piece of technology that is very hard to master.
PG already has its own clustering solution to scale up and down, which is orthogonal to Kubernetes. So running PG in Kubernetes does not add anything. Also, you are much more likely to mess them up when trying to mix two orthogonal technologies.
And the DB is not meant to create and recreate often unless you want to purge the data. So my take is this: Kubernetes is to manage and configure microservices and DBs are not microservices.