I don't like web apps and don't want my life in Google. Also I had been a paid user of Evernote for a few years already when Google Docs came out, I had already learnt that "if you're not paying for it, you're the product".
I'm not a fan of Microsoft, either. I've never had to swap Word documents around so that's not in my lie at all.
Evernote was on my computer, and on my phone; it's where I'd note down an idea when I had it, and since it was there I may as well just expand on it in there. When I'm doing solo comics then most of my notes in EN were collections of vague outlines, dialogue fragments, and photographs of scribbly sketchbook pages; actual writing mostly happened in Illustrator. It was easy to expand that to have a script sitting there in EN, since we were both already used to using it. Plus since EN is about keeping notebooks rather than files it's pretty nice to just have one place that holds all the various words and pictures related to getting from "some ideas we've kicked around" to "a script that I can turn into a bunch of Illustrator files on my hard drive".
This is similar to how there are a lot of programmers who do everything in Emacs. You're already there all the time, and it may not be perfectly built for this, but you can do most of what you need in it, so why not?
If you want to be totally anal about doing it The Traditional Industry Way then you can use a complex word processor template adapted from screenwriting templates and deal with rigid page counts. If you are not working as part of an assembly line with distinct separations between Writers and Editors and Pencillers and Inkers and Colorists and Letterers then your script can a pretty casual thing with simple formatting, and Evernote can handle that just fine. Or at least it could before v10 threw all performance in the toilet for that shitty Electron rewrite.
Lately I have been vaguely fiddling with using Scrivener for roughing out scripts of short pieces, and really need to get my partner on this long-brewing GN still kinda trapped in Evernote to give it a shot. If we can get a decent sync pathway to bring the .scriv files between our disparate devices then maybe my dusty Evernote notebook exports will turn into a handful of Scrivener projects, along with the scattered notes in Joplin and Apple Notes that have happened since I finally said "fuck this abusive relationship with New Evernote".