For a start, people will use derisive terms like “M$” at you.
(Of all the criticisms to make of Microsoft, “they have wanted to make money since the 1970s” is surely the least biting…)
Google Drive, Dropbox, and the equivalent services of Microsoft, Apple, etc are meant for personal storage. They’re great for backing up your project folders. They work well for sharing a test package with a group of testers.
I don’t recommend them for hosting media files for a published game. They are not meant for that; I worry that links to those services will break in the long run.
For example, there was a shift (about 2016) where all of these services blocked the ability to share live HTML. Before that, you could host a Twine game directly on Dropbox and it would be playable. After 2016, you couldn’t do that. (The file would still be present, but it would be displayed as raw HTML.)
You can still host live images or other media files, but what if they block those too? Or make all the links into “download” links? Or put limitations on how many users can view the file in place? Or change their organizational system so that the old URLs no longer work?
These are all reasonable changes for a personal-storage system, but they would break hotlinked media for Twine or other web-playable IF.
Itch is meant for hosting published games, so you don’t have these worries. Of course Itch is a tiny private company without the inertia of Google or Microsoft. So you get to decide.
On the other hand (there are always more hands) you might not be worried about long-term storage at all. If you only need the files to stay accessible for the academic year, the concerns about Google etc are probably not relevant. Most years aren’t like 2016. (Then again, a few are.)