This is actually what I did when I was in school, and overall it was quite pleasant. There was some WYSIWYG LaTeX program too that I shared with some colleagues when we were working on a document together, I remember it working okay.

But I don't see the average student, especially studying non technical stuff, to pick up LaTeX just for normal sort of essays. Even I am fairly rusty now. And honestly I don't even know if I could have managed it during high school, where I had to write English essays and stuff with specific formatting for references. (I am grateful that my engineering education was less strict about that sort of thing).

I was hoping that someone would suggest a self hosted web document suite, I think "Nextcloud" is a popular one. Then it should work on any OS, and you don't have to worry about syncing files. Even if you can pay to have someone else host an instance (not sure if this exists), and ideally a program that can keep a local backup synced to your PCs would be a big step in the right direction. Syncthing seems pretty great, though I haven't used it much, and on iOS it doesn't seem to be able to run in the background.

edit: I just read another comment that recommended OnlyOffice, this seems like another good option (source: this reply: https://lemmy.ca/comment/9415293). Aside: is there a proper way to link to a comment on lemmy that will go through your own homeserver?