> Coq, in particular, is a pretty brutal installation process if you aren't already an emacs user.
It's only "brutal" if you're compiling from source, in which case you've got to compile all of the ML and then all of the Coq libraries. That's only necessary for experimental branches though; I've not used an OS which doesn't provide binaries of official releases.
The installation process is basically "apt-get install coq && coqide", or whatever package manager your system uses. That will run the GTK interface which comes bundled with Coq.
The only time when Emacs might have anything to do with Coq is in relation to Proof General; but the only reason to run PG is if you're already an Emacs user. It's been in maintenance mode for years, and being rapidly overtaken by asynchronous interfaces based on PIDE (eg. the jEdit and Eclipse plugins).
I'm a very happy Emacs user, but just because I use Coq via PG doesn't mean I'd ask non-Emacs-users to do the same; in the same way that I access my GMail account via Gnus, but wouldn't try to convince non-Emacs GMail users to do the same.