...has anyone thought about them?
Here I don't mean the bloated 120-200MB Debian base, but a Docker with something like a light 5MB Alpine base.
LibreElec actually recommended Alpine bases in its Docker add-ons write-up (addons for LE, not LE inside a Docker itself), but Alpine seems to have lost traction with Docker. The problem could be Alpine's musl libc which doesn't play nice with existing compilations.
Alternatively some other container format with a light base should work.