This particular database was not a system of record. The database stored the results of a stream processing system. In the event of a total loss of data, the database could be recovered by re-streaming the original data, making the operation of PG in a kubernetes cluster a fairly low risk endeavor. As such, HA was not implemented.
This setup has been running in production for over two years now. In spite of having no HA, each instance of this application backed by this DB had somewhere between four and five nines of availability while being continuously monitored on one minute intervals from some other spot on the Internet.
During the course of my tenure, there was only one data loss incident in which an engineer mistakenly dropped a table. Recovery was painless.
I've since moved on to another role and can't imagine having to run a database without having the benefits of Kubernetes. I'm forced to, however, as some folks aren't as progressive, and damn does it feel archaic.