There are projects that help you run databases in kubernetes and also make backups of many things hosted:
- Automatic CephFS for your cluster -> https://rook.io/docs/rook/master/
- Backups for cluster resources and volumes -> https://github.com/heptio/ark
- Spin up dynamic postgres clusters -> https://github.com/zalando-incubator/postgres-operator
Databases are just applications with different resource needs. Please stop pushing forward the notion that they can't be run in containers or container orchestration systems. Databases are just programs. If the substrate for running your containers doensn't reliably support flock or fsync or something your database needs, then maybe pick a better substrate that does -- container runtimes these days and kubernetes don't stand in your way these days.