Shooting people in the living room is a modern institution. Shooting people on the bus, at the train station, or wedged into the bath, however, is rather less prevalent.
Handhelds have had trouble with FPS games for some time. In the days of the Game Boy Advance, it was probably mainly to do with technology: Nintendo's chunky little delight may have had 32-bit graphics, but it still struggled to bring even id's earliest titles flickering out of the past.
These days, however, it's more to do with the interface: whether you've got a stylus in your hand or a single runty little analogue nub under your thumb, portable consoles just don't seem to be equipped for headshots and strafing.