The better solution is to use an open door design (often found in airports) and have hand dryers rather than paper towels. Less waste and associated mess, no garbage to change, no doorknobs to not touch.
The Dyson Airblade hand driers are really catching on in the UK in public building toilets. They are fun to use and actually work rather well. However the bottom of the opening where you put your hands gets some cruddy water/residue in it.
But it requires more floor space, which may not be available.
Also, in the vein of the lesson being taught, that may be the "right" solution, but in an existing building, it's certainly more pragmatic to add a wastebin (versus, say, rebuilding the bathrooms).
To my understanding hand driers are less hygienic. With paper towels you actually wipe off some the grime while with hand driers any left over stuff just dries on your hands.
The Dyson ones I've seen have only ever shot cold air on my hands and pushed my hands against both sides of the dryer. Maybe they've been horribly misconfigured at all 3+ places I've seen them at, but in my experience they've just been less effective and less sanitary than both traditional air dryers and paper towels.