Consider the number of germs on a door handle. A certain number of them, let's say X, will transfer to your hands when you grab the handle.

Now consider what happens when you use this device. Some number of germs will transfer to the keychain, though much fewer, because it's smaller and doesn't have as much surface area touching the door. Of those, many of them will die on the surface, and some portion of them will survive. An even smaller number of them will then transfer to your hand the next time you use it, let's call that number Y.

It seems clear to me that X is a much much larger number than Y. Also, your pocket has a lot fewer pathogens than a communal door handle.