Distros are okay with a single starting binary for compilers. Gcc does this, for example. Rust would publish a single bootstrap binary, and distros would build the next compiler with that (and publish), and build the next one with the one that they just built, and so on. Multiple platforms would just involve cross compiling the first time.
The problem, historically, with Rust is that each release was built with the latest nightly, so you had to bootstrap each new version. Now they've changed to using the previous compiler release to bootstrap, so you can bring a binary in for the first build of a package then immediately rebuild with your bootstrapped binary and continue on from there for eternity.