There's already other libraries out there like Fullstory, which tracks all the user mouse movements and interactions with the page and allows you to watch a user interact with your site in nearly realtime.

There are full tracking tools that do a lot more than this already - tracking all mouse movements and key presses. They are often used with the knowledge of users when testing UI changes/experiments, I've even heard of more general versions running as a browser plug-in for medical monitoring (watching for changes in coordination of people with degenerative conditions, without it feeling like an active test accidentally biasing results), though I would also be surprised not to find the idea already used more widely (and perhaps more nefariously) without users knowing.