The installer from https://www.rust-lang.org works fine on Debian stable. Right now, you can just use the upstream rustup.sh script for platforms that don't yet have it packaged (like Debian stable), or install from your distro for those that do (or use rustup.sh on those as well if you like).

What I'm not seeing is the value of a Docker image. Rust doesn't have much in the way of runtime dependencies, which is where the value of a container generally comes in. I don't know of a platform where Docker image would work but rustup.sh would not.