[regnat]

You can install Nix in a totally unprivileged fashion, without having to use hacks such as PRoot, you just need to configure it to use a directory you have write access to instead of /nix. But doing so breaks the ability to use the official binary caches (because relocating the store requires recompiling packages), and this isn't particular to nix (I remember that portage at least does this too, and probably some others). The interesting part is that with an installed deamon, the admin can allow users to install packages in their own profile, while still benefiting from sharing of dependencies and other niceties.

About the multiple versions, the problem with "classical" package managers is that you have to do some manual renaming to ensure that both versions won't be installed in the same place in the file-system, which is tedious and doesn't scale well. Furthermore you may encounter some problems because both will be visible at the same time if the packager isn't careful enough. For example, if a software X has a dependency of libfoo2.1 and you happen to have libfoo3.1 also installed, the installation script for X may use libfoo3.1 instead of libfoo2.1, in which case you risk to encounter bugs because X hasn't been tested against libfoo3.1.