I know very little about dragsters, but here’s what came to mind. I would say they use parachutes....
The NHRA requires parachutes over a certain speed. The most important reason they are used is because they provide directional stability while slowing the car. With the lack of suspension, very long wheelbase, narrow track, and extreme rearward weight bias there's no way a top fuel dragster or funny car could safely stop from over 300mph by only braking the wheels, they would lose control. Some fighter jets and the space shuttle use drag chutes for the same reason.
But I do agree that they look totally cool. Plus they provide plenty of square footage for sponsorship advertisement.
I'd agree with the directional stability reason - afterall, parachutes aren't the most efficient way of actually decelerating the vehicle.