Ironically, doesn't Homebrew build everything from source? So in that case it would end up installing the Rust compiler before building the application... What you want is a binary download, it seems.
Although many packages are still source only, Homebrew has an initiative for packaging (or 'bottling') larger tools into binaries for convenience. It can always be overridden with --build-from-source
No, homebrew supports pre-compiled binaries (known as bottles).