While I tend to agree that there would at least be less friction if people just installed it from us, distros are going to package it - it's what they do! So I'm inclined to do what I can to make it a decent experience.
It will not. Though I can imagine why one would want that, could you say more about why that is desirable?
Is downloading and building in an arbitrary location the common way to build both user-contributed and official packages from source? IOW there's no single command that just does both? Is there any automatic mechanism for enforcing build deps, that is, that the rustc package is installed?
Does the /etc/profile.d/ script take effect automatically? I agree that this looks promising.
Publishing the binary isn't something I've considered carefully, but it does result in no proxies, which are a core part of the design, and a scenario I haven't put any consideration into until now. One could imagine being able to bootstrap the rustup install via the system cargo, then having an option to later generate the proxies. Though off the top of my head I'd prefer in this situation for the proxies to still exist and to default to the system toolchain.