Docker volumes are great. I've also run databases in docker without issue. But they're different from kubernetes "persistent volumes" and "persistent volume claims"

The issues come when you move into high availability (specifically in a Kubernetes context). K8s may decide to move your database to a different node (server) on a whim, and suddenly your data is gone. You have to solve this by having mounted, block-level storage available to your cluster (eg AWS's EBS; the product being discussed) so you can use persistent volumes. That comes with added complexity, and usually the need to incorporate db operators into your stack.

As a result, a lot of k8s admins (myself included) choose to pay crazy amounts for RDS and S3 to avoid the complexities of persistent data.