> Also, ideally, you'd publicly host the Dockerfile

Docker doesn't make it easy to produce a reproducible config. People commonly write Dockerfiles with stuff like this in them:

RUN apt-get install -y my-favourite-package

And then which version of my-favourite-package you get depends on what is the latest one on the update servers at a time. Maybe a new version is released tomorrow with a regression bug that breaks everything.

There are ways to get around this problem, but the default ways of doing things in Docker doesn't encourage reproducibility.