Their primary benefit is lower cost of operation for the facility, but other than that, their environmental impact is at best marginally better than paper towels, and worst is their hygienic aspect.
Various studies have found up to a two-fold increase in bacteria count on users' hands, as well as a risk of contaminating the surrounding area with bacteria blown off of the user's skin:
"In 2009 a published study was conducted by the University of Westminster to compare the levels of hygiene offered by paper towels, warm air hand dryers and the more modern jet-air hand dryers. It found that after washing and drying hands with the warm air dryer, the total number of bacteria was found to increase on average on the finger pads by 194% and on the palms by 254%; drying with the jet air dryer resulted in an increase on average of the total number of bacteria on the finger pads by 42% and on the palms by 15%; and after washing and drying hands with a paper towel, the total number of bacteria was reduced on average on the finger pads by up to 76% and on the palms by up to 77%." [1]
The noise aspect discussed in this article is yet another reason air dryers need to die. I hadn't even considered the effect they might have on kid's ears, and I'd imagine most adults probably haven't thought about it either. I find them positively annoying, but having your ears at the same height as these monstrosities must be horrible.
Kudos to Miss Keegan for her wonderful research!