alt Hacker NewsDocker Compose (ignoring Swarm which seems to be obsolete) manages containers on a single machine. With Kubernetes, the pod that hosts the database is a pod like any other (I assume). It gets moved to a healthy machine when node goes bad, respects CPU/mem limits, works with generic monitoring tools, can be deployed from GitOps tools etc. All the k8s goodies apply.
When it comes to a DB moving the process around is easy, it's the data that matters. The reason bare-metal-hosted DBs are so fast is that they use direct-attach storage instead of networked storage. You lose those speed advantages if you move to distributed storage (Ceph/etc).