The PostgreSQL operators are definitely usable, pretty much none of their limitations are going to hit you on an MVP. I think a lot of the FUD about "don't run databases on kubernetes" came from a time before we had statefulsets and persistent volumes.
Which operator did you go with out of curiousity?
I'm using the Zalando one. It only took a couple of hours to get it running (first time running it) and integrated in graphana. Includes incremental backups to S3. It really feels like a cloud independent managed database.