I just saw a breakdown of a crash where the engine shut down, allowing the clutch to stop slipping. That final clamp dumped a huge impulse into the drivetrain and ripped the tires off the wheels. (At least that's the way I understood it).
The clutch slips for about 2/3 of the 1/4 mile. It is a huge factor.
My college motorsports team got to meet with John Force, and someone suggested a flexible rear spoiler for variable downforce. He was quick to note it likely would be faster but would almost certainly get you killed.
its my understanding that the clutch designers are the highest paid crew members. Choosing how the clutch performs is the critical piece to winning, based on track temperatures, weather conditions, engine performance, etc.