We are running a handful of stateful services in K8s (things like MongoDB for which GCP doesn't have a compelling and affordable managed offering). It's definitely more complex than transitioning a stateless service, but so far our experiences with StatefulSets and PersistentVolumes have been good. And this allows us to sunset Puppet/OS management completely. I should note that we _are_ being extremely careful about backups. We also run each stateful service in a dedicated node pool for isolation. Who knows, maybe a year from now we'll be shaking our heads and saying "that was a TERRIBLE idea" but for now, so far so good.
We're running on GKE, so lots of things that would be hard in on-prem environments (ingress, networking, storage) are easy.