I have had the exact same experience as the OP and if you can convince several PI's with better things to do than reinstall a new version of Word, people at other institutions without MS Office licenses using Libre Office and others who don't use either and convert it back and forth to a Google Doc (thereby breaking all the hyperlinking), I would honestly be baffled.
Now, in collaborative work I use Overleaf so there is no configuration problems with installing LaTeX (Google Docs for LaTeX), and give everyone write access if they want it, I sync it with my Dropbox and have a working LaTeX distribution if I want to edit without access to the network. Those who don't know LaTeX (which is a small number, especially if they don't want to learn the basics to edit the .tex file in the appropriate place) I can convert a version to Word for their edits, which I then incorporate, or they can just markup a PDF. The Overleaf document then has a complete history of edits, Overleaf supports Word-style comments and track changes, and I can be happy in that the other authors aren't going to break something in the Word "backend".
I guess if you trust DropBox and Overleaf with sensitive data but not Google Docs or Microsoft Office 365, that works. (If Overleaf is self-hosted, please disregard that part.)
I also find offline word processors frustrating to collaborate on, but I am worried that OP is rationalizing their personal preferences post-hoc, rather than looking for the best option for everyone.
Thanks for the pointer to Overleaf, I will definitely check it out.
Yeah, not the OP, but if I had sensitive information I don't know what I would do. I know this sounds shill-like, but I absolutely love Overleaf for Latex. It has every package you need, decent templates that you can then customize, and the Dropbox and GitHub integration are great - uploading an image is as simple as saving it in the right Dropbox folder - very useful for when trying to upload a bunch of images or update a figure in Illustrator. I end up using MikTex like 2-3 times a year when I'm on a plane, and then everything syncs once I'm back online. Being able to see who changed what is also great, and much less overhead than trying to convince non-programmers to use git or something like that for the Latex files.
With LaTeX, you can track your changes in git, collaborate in online platforms, use your favorite editor, perform diffs/merges with your favorite editor. With word processors, you are stuck with 1 editor and few live collaboration options like google docs and word online which have a reduced feature set.
Now, in collaborative work I use Overleaf so there is no configuration problems with installing LaTeX (Google Docs for LaTeX), and give everyone write access if they want it, I sync it with my Dropbox and have a working LaTeX distribution if I want to edit without access to the network. Those who don't know LaTeX (which is a small number, especially if they don't want to learn the basics to edit the .tex file in the appropriate place) I can convert a version to Word for their edits, which I then incorporate, or they can just markup a PDF. The Overleaf document then has a complete history of edits, Overleaf supports Word-style comments and track changes, and I can be happy in that the other authors aren't going to break something in the Word "backend".