You know, I grew up reading the comic strip, which is very dark and would not likely lead children to believe that life is rosy or that salvation by a 1%-er is the key to happiness. In the comics I grew up with, Annie confronted all manners of predatory humans and stark cruelty — AFTER she was adopted.
So I never really connected to the Broadway musical. It not only seemed impossibly optimistic to me, it seemed more loosely connected to the source material than even other musicals that take a lot of artistic license.
But as you say, it's EVERYWHERE. I think it answers a human need for optimistic fantasy. Escapism. Something like that.