If you're offering a new package manager up for installation (which, Steam aside, isn't the kind of thing that's normally practical to put inside a Flatpak sandbox) on a platform where every distro has its own package manager and repository, what would you propose?
There's a reason they offer "download and run this .exe" on Windows and "download and run this .sh" on POSIX platforms.
...plus, as they mention in the tiny "other installation methods" link, none of the distro packages are official and people have a nasty habit of coming to you for support even if you didn't point them at the downstream-patched distro package they found.
Given how much distro packagers have tried to contort Rust to fit into their pre-existing `.so`-centric packaging system, I can see why Rust upstream would want to downplay that option to avoid headaches.
Let's compare what some other supplementary package managers tell people to do: