There are no "bash plates" under a regular drag car, a wheel stand coming to an abrupt end still means damage, depending on how abrupt. Most drivers don't step right into a car that does a 6 foot high wheel stand for their first pass though. A lot of effort is spent getting the whole set-up right as well - shocks, springs, bump stops, suspension travel and ballast all play a part. Couple that with practice with launch rpm, shift points, gearing, tire pressure, etc. When it's all done right with an experienced driver it's a thing of beauty. And remember many are pulling a shift while it's in the air! John Calvert's original '68 428 CJ Mustang is a veteran of thousands of airborne passes.
I would guess that some of the cars you see competing at these "extreme" wheelie events where they are judged by crowd reaction to the carnage might be set up with some kind of skid plate, but nothing under your typical NHRA / IHRA stock or super stock car.
