I'd think the egg is used to act as an emulsifier. I don't think bananas are an emulsifier? Are they? Would make sense you'd need something that will force water and oil to mix when making Brownies....Hrmm, I wonder if those oil/vinegar dressings that never need shaken contain raw eggs. I will have to look.
BUT, Brains are an emulsifier! Well thats one reason why you use them to tan hides, LOL
By no means should you use brains in brownies though, LOL