We did this in the Gravity Kubernetes Distribution (which development is shut down), but we had to for the use case. Since the distribution was used to take kubernetes applications behind the firewall with no internet access we needed the registry... and it was dead simple just running the docker-distribution registry on some of the nodes.

In theory it wouldn't be hard to just take docker-distribution and run it as a pod in the cluster with an attached volume if you wanted a registry in the cluster. So it's probably somewhere between trivial and takes a bit of effort if you're really motivated to have something in cluster.