I'm not sure why you'd need the users permission to view what they're doing on your site in real time? I don't feel like I need to gain permission before I tail my access log when people are viewing my website? How is this any different?
The "someone" is the person running the website. So no, of course I don't mind. What is the danger?
I already leave a log of my IP address, the web browser I'm using, the links I click, the time/date of my visit and any data that I submit through forms. If they want to monitor my mouse position as well, then fine.
You're talking about small websites. I'm talking about websites with a lot of traffic and a lot of employees. You think only one person will be using that function? Not to mention the potential abuse by employees whose job is to monitor real-time user activity.
I'm all for securing your privacy. I'm just not one of those people who thinks my privacy is being invaded if somebody looks at me when I'm walking down the street.