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.