TL;DR: People be dumb.
I honestly barely pay attention to BIll Nye because I used to watch him on Almost Live, so it’s basically impossible for me to take him seriously, so you’re asking the wrong person.
Admittedly, I never watched Bill Nye Saves the World, so I don’t know firsthand how egotistical (or otherwise) he was. But still, that title alone says something…
I did watch the obscure Planet Green show Living with Ed, however, in which Bill Nye was portrayed as the rival/antagonist and kind of an asshole. Who knows how much that was being played up for the camera, though.