This is such a good question. Thank you.
So, a little backstory. Ever since Google removed their motto "do no evil" they have gone down the rather predictable path of all big players of the rot economy: putting profits over user experience.
A little while back, there was rumor that Google trains AI with the content of google docs, then they said they don't really, they only scan the content and do nothing with it, and then they started blocking access to documents with sexy images. Do we believe that Google has our own best interest at heart? That's something everyone has to decide for themselves.
Back then, I made a post with alternatives for Google Docs, you can find it here, also check the reblogs for more options:
Now, is it a good idea to switch from google docs? I think it is, but I'm also not consistent with it. As you mentioned, it seems to be the easiest to share writing with beta readers, and I also still often use it for fanfiction.
But there are alternatives, and they require very little adjustment in the process. Let me give you two free options.
Ellipsus is webbased, meaning you can write in it in the browser on any device. They have sharing, specifically for beta reading, and an export function for AO3.
Reedsy (marketplace around everything self-publishing) has an editor. It is webbased, and they also have an option for sharing with beta readers. This software is aimed at book type-setting and exporting but it works just fine for copying to web.
Personally, I'm currently switching everything to LibreOffice (also free!) files in some cloud connected folder. I used to do a lot of mobile writing on my phone with a bluetooth keyboard but currently, I'm taking my laptop everywhere so LibreOffice works great for me. If I have to use my phone or tablet for some lightweight mobile writing, on vacation for instance, I can still use something webbased.
So, I hope I gave you some interesting options. Do I think it's a good idea to make us less dependent on Google? Yes, I do. I don't trust them.
We have alternatives, and they cost us nothing more than a little adjustment.