Meatballs started out in life as a poor man's food. Adding bread crumbs or stale bread soaked in milk was a way to stretch the meat to feed more faces. This addition resulted in meatballs with a different, more tender, texture from an all meat meatball, which would be a firmer, chewier item.
The addition of bread/crumbs and moist ingredients made the addition of egg more important as a binder.
That being said, do whatever you want. If you like heavy firm meatballs, that's OK. If you like lighter, softer meatballs go another way.
Basically if you make meatballs you like and they stay together without egg. Great. If you're having a problem with their breaking up, add egg.
"If you want to make an apple pie from scratch, you must first create the universe." -Carl Sagan