Debian has made a tool, "debcargo", to automatically turn crates from crates.io into Debian packages, so it should be "just run this tool." I have not used it myself though.
Anyone releasing software in C, Python, Haskell, Ruby, Lisp, or whatever language has extra work to do. I don't think there's any sizeable difference between any of them.
Distributions such as Fedora and openSUSE need to have a package for everything installed on the system (and everything required to build said packages). Now take into account the you can have multiple versions of the same library in a single rust project. While you could handle all of this on paper, automating it and putting it all into every distributon's build system is a very big task.
Ruby has similar problems, NodeJS is even worse than Ruby in this respect but I believe that Rust might make this the hardest for distributions. Personally I've never liked cargo that much as a user either, but as someone who works on openSUSE and was thinking about packaging rust packages I decided against it. It's just far too difficult and I'm not convinced it's worth the effort, since it feels like people have forgotten the reason why distributions exist in the first place (to provide a cohesive experience and provide you seamless management of your software). Having a shiny new package manager for every language just makes life difficult for everyone involved.
Fixing that is a big focus of this year https://github.com/rust-lang/rust-roadmap/issues/12
Oh, I thought of something better than just the compiler: https://github.com/burntsushi/ripgrep#installation
* homebrew
* chocolatey
* arch
* gentoo
* fedora
* RHEL/CentOS
* Nix
All have at least one Rust program packaged :)
And even then, having the compiler and package manager available is a step along the way, but insufficient. Anything non-trivial depends on libraries, which with C programs are typically also packages... which for my project means I need to create 73 Debian packages to distribute my software. That's a big hurdle.