They’re busy people and in many cases very influential (and probably also wealthy), but famous people are still people at the end of the day. As a fan of few people in this world, when I do get the chance to meet them, I try to approach them as a human first and a famous person second. Another way to look at that is: great every stranger you’d like to make a connection with with the same respect you’d treat your heroes. If you go up to them and start freaking out because you’re actually talking to them...how do you think that feels for them?
I’ve always thought that it wouldn’t be that fulfilling to be famous, because you’d lose the opportunity to do things like go out to a normal restaurant with your family and have dinner without people acting weird around you constantly. Paparazzi are one thing, fans and stalkers another.
TL;DR don’t be the person who makes being famous suck, and you’ll probably get a lot more out of having an interesting conversation with someone you look up to vs just getting an autograph.