At the mall here, one bathroom has a really good air dryer where it blows your skin so hard you can see your bones, and it actually does get your hands dry, and in a reasonable amount of time. And instead of doors, it has a hallway with a corner, so there's no handle to touch, and you can actually come out of the bathroom knowing your hands are clean. That is definitely the ideal.
However, most air dryers suck and end up making you need to wipe your hands on your pants, which is unsanitary. Most bathrooms also have doors, usually opening into the bathroom, meaning you must grasp the handle to leave. Some even have two doors in a row, as a sort of airlock. Without paper towels, you must directly touch the handle, and the handle is small enough that you will be touching it in exactly the same place as everyone else, and half of grown-ass adults don't wash their hands after using the bathroom. So I guess, for pragmatic reasons, I must pick paper towels. Because when there are paper towels, you can use them to open the door without making direct contact with the handle. But a really good air dryer in a doorless bathroom is definitely better (though there should still be paper towels for if you need to clean something or something).
(also, toilets and sinks should be able to be operated by foot pedals)