Requiring distopian spyware doesn’t weaken your brand. It destroys it. For most of history, reputable universities built their brand just fine without any software at all.
It’s basically up to the instructor on how to run the class.
Some require proctorio, some are on Zoom with lots of TAs to watch the screen, some issue an exam on your own time where the browser monitors what you do / visit, and others just offer take home projects.