Mobile Gaming controls idea

Speaking of controllers, could a phone improve the possibilities of controlling a game (and therefore the games possibly available/enjoyable on a phone) through the idea of back-side paddles or back-side controls of some sort?

Not speaking of sticks protruding from its back, but… I think I can imagine myself holding the phone (horizontally) in between my thumbs and ring+pinky fingers, while:

1-moving with my left index behind the phone

2-looking around with my right index behind the phone

(these can be mirrored for lefties if needed)

3-using my two middle fingers to “press buttons” on the back (what would be called paddles on a regular elite controller of sort)

Therefore I wouldn‘t have to put my fingers directly on the screen covering the videogame itself that I’m looking at.

The two so-called "sticks and paddles" in this case would be sensitive spots on the phone surface on the back of it that could be fully slotted in the phone chassis (to avoid having protruding pieces on the back of the phone, maintaining its minimal 3d shape)

mmmm What do you think?