ps4 controllers are generic bluetooth gamepads that I've been able to connect to a surprising range of devices.
On phones with the feature, you can use your left thumb to walk, right thumb to aim, and 3D touch (press down hard on the screen to shoot). I know at least call of duty mobile supports it, and when I tried it out it felt revolutionary.
But rather than add new input methods, they’re removing them at the same time they’re trying to push harder into mobile gaming (with Apple Arcade).
It’s baffling as an outsider to see such obviously bad/stupid decisions like that from such a massive company.
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
Most action games require at least 3 simultaneous inputs to be played effectively.
There's definitely workarounds like the ones you mention, but unless a game is actually made for touchscreen controls, as in optimized for no more than 2 simultaneous inputs, it's not going to be as playable on a touchscreen as it would be with anything else.
Unfortunately, some genres of game just aren't as suited to only 2 simultaneous inputs.
There's lots of fun touchscreen based games, but they're always better with game mechanics specifically suited to touchscreens.
Disc: Googler.
The price isn't out of line even if you consider it as a "thin client" gaming device.