Manu became a 6th man for the same reason that exists today: Tony Parker.
Manu plays best with the ball in his hands most of the time. So does Parker. If they start, they rest at similar times and you have less capable guys trying to run an offense and produce points.
Why not bring one off the bench? Why Manu? Because he's a great distributor and runs the offense. He makes others better around him. Like you said, usually the best players start... that means the guys coming off the bench are not as good. He is the kind of player that makes them better. And he can go to town and take all the shots he wants, because he has that green light to maintain leads or cut into defecits and he is the most capable player on the court to do so (at least when the starters are sitting).
And you do want your best players on the court at the end of the game, which he is anyway.