It's all about the Xs and Os.
What happens when Parker drives? Well, for one thing, the entire defense of the opposing team collapses on him. This means that if he gets out of position or he misses, they suddenly have 3-4 players around the boards for rebounding.
Even if they -don't- collapse, if you'll watch, Parker goes to the opposite side of the bucket that Duncan has posted on (Duncan usually posts to the left side in this case). This means that there is not only a defender with Parker near the hoop, but one between Duncan and the basket, assuming they aren't fronting him. If Parker misses, or even if he passes to a teammate for a shot, the other team has effectively pulled in a bit. Duncan doesn't want to go over the back and pick up a stupid foul, so he has to give up the space and the rebound.
Compare this to the Tony Parker that drives and dishes. Now, he has a step on his man (who has to follow him out of the post), the defense has fallen back a bit, and we have open shooters who can move the ball just about anywhere. Since Tim doesn't have to worry about being in Parker's path when he drives, he can repost for better rebounding position if we miss.
As a side bonus, we control the game clock a lot more in this case, which means less time for the opposing team to have the ball, which means our defense will yield fewer PPG.
As a second bonus, Parker will most likely be fresher for the 4th quarter, meaning he can play better D and have better penetration. I've noticed that teams make almost as many adjustments to Parker now as Duncan. If you wait till the 3rd and 4th quarters before letting him loose, you could surprise a lot of teams who think they've been able to stay in front of him the whole game.