I do remember a game that did something like that many years ago (posted on reddit I think?). It was an endless runner type game with a fox character IIRC, and you had to alternate taps on the back of the device to get it to move. I do remember that I couldn't get it to work reliably though.

Tapping the back of my phone now, I can see it maybe working for some types of games/shooters where you don't have to hold down the fire button, if implemented well (which probably isn't easy to do for all hardware). The tactile feedback of smacking the phone could help provide a good experience if paired with appropriate audio/visuals.

This isn't quite the same thing, but the Playstation Vita has a rear touchpad, and not a ton of games managed to use it well, even with the much higher precision (Tearaway[1] is the only good one I can remember).

Tearaway gameplay: https://www.youtube.com/watch?v=Jw5LD4B-3DI