That said, there are fundamental rules of discipline (run 4 miles today for fitness....nah, there's no coach, not today), positioning (I like to play center forward...but so do most of the other players. Who wants to be a midfielder that runs miles every game?), and team management (pick a starting lineup. Decide on substitutions) that just can't be performed by children.
Ideally, kids would like the game enough to want to play it on their own.
I'm sorry, but I think you are flat-out wrong about this. Kids will figure it out. If they aren't old enough to figure it out then they aren't old enough to play the game at that level of organization, discipline and management.
Personally, I don't think kids should play organized sports (and by this I mean "organized" by adults) until they get to high school. The only exception to this might be a sport where an adult gets involved as an official (but only if the kids think it's absolutely necessary).
The best ballplayer in my circle of childhood acquaintances was one of my younger brothers. He never played Little League, and never played any organized baseball until high school. What he had done previously, though, was spend 3-4 years playing with kids several years older than him (my friends). By the time he got to high school at the age of 14 he had already been playing with kids who were 15-17 years old -- and it really showed on the field.