I did have an FO flip out that we declared after we lost 1 of our 3 hydraulic systems (the one that provides 1/2 of the brakes) because he didn't want to have to do all that paperwork when we landed and it was going to make us late for the overnight. Ummm... sure.
Seriously....I have YET to see this mysterious "mountain of paperwork" that people are so frightened of when it comes to emergency declarations. I certainly never carried the "mountain of paperwork" folder in my ARFF truck back in the day to give to the pilot when everything was said and done, and I never saw airport ops people with that mysterious folder either.