Dunno if I ever told this story here, but I've told it many times when I've done presentations. The only "lots of paperwork" situation involving an emergency I have encountered was one where the pilot didn't declare. It was probably 15 years ago. A jet pilot had a flameout in the clouds. He handled it but did not key the mic even long enough to say, "[Tailnumber] unable to hold altitude, MayDay!" I wasn't in the cockpit and certainly don't him for aviating first (and ultimately neither did the FAA) but there was a bit of paperwork, not to mention aggravation and worry about his career, responding to the enforcement action the FAA started for the Class B altitude bust. It went all the way to the attorney conference stage in the process before it was resolved. I'm absolutely convinced that if he had keyed the mic, it would have been a complete non-event, enforcement-wise.