In fact I do like to stare at people, but only from far away and I have no idea what is the utility in that because I am not aware of my brain processing any valid information although I am sure it is doing something.
But I almost never do it because I know it is rude and uncomfortable for them even if they are far away; somehow people have a six sense that tells them when someone is staring at them.
Did it ever happen to you that out of no reason you just turn your head and you see that someone is staring at you? Or you are staring at someone from far away and the person suddenly turns to you?
When this happens I get really embarrassed

so I avoid it, maybe even too much, because I think that Humans being naturally social are inclined to observe others, so why shouldn't I?
I read somewhere recently that Germans ( I live in Germany currently ), specially older ones, are known to be in the windows for large number of hours watching what the neighbours are up to

So I guess this is also a cultural thing.