Making static binaries is often extremely painful and confusing. It's easier on a distribution like Alpine, and nicely enough, Alpine comes as a Docker image.
In general, Docker's ability to basically spin up a whole Linux distribution, with a whole root file system, makes it very different from just using static binaries.
Along with Docker's image repository infrastructure, it makes some things easy that weren't easy before. Like, I don't know if there is a static binary build of the Erlang runtime system, and I don't know what kind of file system tree that system needs, but I just now opened an xterm and typed "docker run -it --rm erlang" and got an Erlang 9.0.2 shell.
I intend it to be a starting point for a conversation, someone who really understands it will be able to convince the skeptic that I play, someone who is just typing the commands because it's trendy won't. Also it helps if they know what a statically linked binary is.
I like containers as a concept, and I like the Docker commands for building them and running them locally. I am less convinced by Docker Swarm as a Prod-grade runtime environment, and skeptical that Docker the company can build a viable business out of something that will rapidly become a commodity, I expect the file format will long outlive the company that created it. But those are nothing to do with the question really, which can be answered purely technically.