Docker doesn't require you to run an entire distro in your container. It's what a lot of people do out of the box because it's convenient and familiar. But as far as docker is concerned your container can be a single static binary in an otherwise empty directory.
There is a growing trend of people building micro-containers with just the bare minimum for their application. Docker is facilitating that trend, not preventing it. If only because it explicitly encourages thinking of containers as application-oriented, not machine oriented.
not saying Docker prevents it but it is hardly widespread. Unless you use Go or a few other languages your toolchsin won't even create static binaries for a start.
There is a growing trend of people building micro-containers with just the bare minimum for their application. Docker is facilitating that trend, not preventing it. If only because it explicitly encourages thinking of containers as application-oriented, not machine oriented.