Don't touch that door handle
I can't even guess why I have never seen this next idea anywhere. I think it would be a great idea to install "wet nap" dispensers in all public restrooms right by the exit door.
The design of it can vary from individually wrapped wet naps to a pop-up dispenser, similar to how a tissue box works. You can grab one on your way out and clean your hands off after you wrap your freshly washed hads around the germ ridden door handle. Or even use it to grab the door handle. Imagine the passing of germs that this will help cut down on.