I see it uses busybox. Does this mean it's for low-spec instances and embedded devices, or did they base it on busybox because shellshock only affected GNU Bash and they felt the GNU tools couldn't be trusted anymore?
It is mainly about size on the base install, long before shellshock. Many use cases only need basic tools, eg configuring the Alpine system itself.
If you have no reason to interact with the userland tools inside a Docker container, you similarly have no reason to introduce their complexity and attack surface in a container designed to run one service.
My current "minimal" installation shows 25 SUID binaries (a large amount of them being systemd related...) and my server services need very few of these.