The software is only running during the test. Most students install it on their main laptop, and they don't seem to have much problem with that. It runs with elevated privileges (so it can make sure it's the only program running), and it's proprietary, both of which I have objections to, but unless I'm missing something and Proctorio is quite different from the software I've used, I don't see much problem with it. In Covid-19 times everyone puts up with things they don't like.
OK then at all, i can't see the problem. Unless there is a reasonable suspicion that it's malware and infects your machine with something that still keeps tabs on you when it's as if not running.