Depends on what you're using your cluster for. When you're big enough it's worth just treating the database like any other job and running it on the cluster, but this can be tricky to get right. For small K8s deployments many people choose to outsource the database to their cloud provider and have it separate from the cluster as there are fewer things that can go wrong.

And why did you thought this?

With an operator, you get HA setup with switch over etc. basically for free.

I would prefer relativly cheap managed db over hosting it myself but its absolutly fine.