The only downside I see is that I need to share my screen with a person I don't know. Don't get me wrong, but I normally have access to some crypto on my laptop, banking notifications turned on for my 2FAs, private messages I'm getting from my spouse, maybe some borderline NSFW chatgpt dialogs, screenshots of my ideas, emails, private notes, personal projects, whole bunch of tabs I am not willing to close or share, etc.
I don't have issues to show the screen to a friend of mine. Or showing the screen of a work computer to a colleague. However, demoing the whole screen is violation of privacy. Please don't do that, unless you grant VNC access to a machine with a set of popular tools, code editors, etc.
How about reverse bug squash? Interviewer shares the screen with all his/her private info, notes, tabs, development environment settings, shell command history (with maybe autosuggestions turned on), and the interviewee needs to guide the interviewer towards finding the bug?