Actually, BOTH the playwright and the head producer(s) receive the award. They are co-winners.
I think the reason for doing this differently than musicals is because some might argue that a musical can have a great book and score, but due to direction, choreography, and design still not be as much of a overall theatrical achievement as another (think Ragtime vs. The Lion King). However, plays often fail or succeed on the playwright's script. If it's a well-written script, it's mostly up to the director, designers, and actors to not screw it up. That said, highly theatrical non-realism plays (i.e. Curious Incident), are, I have to admit, exceptions to this.
It's an imperfect way of doing it but hey, arts awards are stupid anyway.