How is giving something, that is nondeterministic, access to your web browser a good idea? How do you guarantee that it doesn’t enter sensitive information without the user’s explicit consent? How do you guarantee privacy and security?
I’m skeptical, but I am genuinely asking and willing to listen.
As others have said, at this point you don’t have a whole lot of choice; you pretty much have to use what the school provides you.
BUT, what you can do is try to rally other students to your cause. You pay the university, which means that students in numbers have influence over how the the university operates. I think your best chance to enact change is to create a petition to get the university to change to a more privacy-friendly alternative, and put together a proposal on how google and microsoft are harmful, and why your proposed alternative is better.
How is this different from the Firefox extension called ‘Session Manager’ that exists?