>this is overkill right?!

My Ops brain says "Taken in vacuum, yes" However, if you make other things that are not static, put them into a container and run said container on a server, keeping the CI/CD process consistent makes absolute sense.

We run static sites at my company in containers for same reason. We have Kubernetes cluster with all DNS Updating, Cert Grabbing and Prometheus monitoring so we run static sites from nginx container.