I always thought closing the lid improves the flavor.
Of course it does... and it decreases cooking time. And also minimizes the amount of BUGS that may fly thru and fall into what you're cooking.

But tonight I saw Good Eats on Food Network about
infrared grills that're supposed to cook in half the time, and it doesn't matter if the grill lid is open or not. Sounds cool... but not sure if they increase flavor like a standard grill, though.