You need to think a little longer about how FPS games work. The crosshair stays fixed in the center of the screen, and you use the mouse to move the character so that your target is under the crosshair. There is no mouse pointer. How would a touch screen even work?
Besides, your fingers can move a lot faster than your whole arm. Even if there was a practical way to get a touch screen working, most good players are accurate to within a couple pixels with the mouse, so I can't see there being any sort of advantage to the touch screen.
You'd also have to have absolutely everything except the fire button mapped to your left hand. How would you turn/run/strafe?
You would have to have everything except fire mapped to the keyboard.