The Edge is too cool, there is no doubt about that. He's brilliant, funny, good looking and modest, which not something you can say about each of them (the modest part). Class just oozes out of Edge. I can't imagine him saying things like "We're the coolest people out there, we're the greatest band in the world, we're ____ awesome!" He's too cool to do that. If he ever releases a solo album I'll buy it the day it's released.
The coolest thing about The Edge is the coolness of his cool.
Did I use the word "cool" enough? Yes, that was corny, I realize that.