You can spend a lot of time getting databases and other stateful workloads to work -- mess around with StatefulSet and PVC on top of all the normal Kubernetes concepts, and what do you get in the end? Are you really better off than you would have been if you ran the database in EC2?
Plus, "herds not pets" kind of breaks down once you start using StatefulSets and PVCs. Those things exist to make Kubernetes more like a static environment for workloads that can't handle being run like ephemeral cattle. So why not just keep using your static environment?
If Kubernetes is the only workload management control plane you have, then I guess this makes sense. But if you are already able to deploy your databases with existing tools, and those existing tools don't really suck, it's probably not worth migrating. It would take a lot of time and introduce significant new risks and operational complexity without a compensating payoff.