Because I'm trying to move the mouse on the screen, even if I get the op-amps to improve the signal I still only have 1024 different values on X and Y axes. With PC resolutions going easily up to 3200x1200, I would need more than that to get 1 pixel accuracy.
An acceleration sensor will not produce absolute position data, like x-y coordinates. It will rather produce data about the rate of change. A big difference! That's one of the reasons why 10 bit resolution should be absolutely sufficient for this purpose.