For me real-time is useful in 3 applications; 1) Error monitoring like site down. 2) System checking, like checking analytics is working directly after setup.

For me real-time is useful in 3 applications; 1) Error monitoring like site down. 2) System checking, like checking analytics is working directly after setup. 3) Amusing/impressing non-tech types that they can see who is on their website at that moment when I try to explain the value of analytics.