This seems completely incompetent on Apple's part and all-around awful. The supposed point of these prompts is that somebody could install screen recording software on your computer without you knowing. Now, that person can defeat the prompts, while everybody intentionally installing software has annoying hoops to jump through. Worse, they might have a false sense of security when it matters the most.

I hope these prompts get removed but, if they exist, they should not be possible to sidestep.