Right, that's usually described as "forwards compatibility", and yes, rust the language doesn't attempt to supply it. And yes, rustup is in fact a (the) solution for users. Distros increasingly package it because it is the recommended way to use the rust compiler (e.g. if you're on the latest ubuntu or any of its derivatives you can install it with apt instead of curl|sh).
A decent portion of projects, especially bigger ones, will try to support stables going back a few versions, but at best they're just changing the timeline slightly. This is really intended to help packaging for distributions, not users. Users should just use a compiler at least as up-to-date as the software they are trying to build.