Cargo install was never intended to be used that way. It's for things useful for Rust developers, not for people who use a program who happen to be written in Rust.
There's a few things at play here. For "build from source" distros, we've been making some changes to make it easier to package rustc. Namely, instead of relying on a specific SHA of the compiler to bootstrap, starting with 1.10, it will build with 1.9, and 1.11 will build with 1.10. This is much, much easier for distros. As for Cargo dependencies on those packages, we'll see. There's a few ways it could go, but we need the compiler distribution sorted first.
A second is that we'd like to eventually have tooling to make giving you a .deb or .rpm or whatever easier: https://github.com/mmstick/cargo-deb is an example of such a tool. This won't necessarily be good enough to go into Debian proper; I know they tend to not like these kinds of tools, and want to do it by hand. But "Hey thanks for visiting my website, here is a thing you can download and install", these kinds of packages can be made with this kind of tooling.
In general, it's complex work, as then, these issues are also different per distro or distro family. We'll get there :)