Does it buy you much though? The big issue with databases is storage, and you need local storage for optimal performance.
You can ask k8s for a persistent volume on local storage, but at this point you have to treat that pod exactly the same way you'd treat a snowflake database server, because the local storage is what ultimately matters.
You can replicate to other pods with their own persistent volumes, but the replication overhead adds up too both in terms of performance and complexity.
I know there's stuff like vitess and crunchy data, which try to abstract this away, but the amount of layers buried here is very high for benefits that seem kind of nebulous compared to "big ol server" mode.