The only real reason having a Lefty at QB can screw up your offense is if his backup is a Righty — at that point your offensive line is a mirror image of what your backup requires.
As for Lefties being “less accurate” — I don’t know where you’re coming from with that.
He'd be handing the ball off to running backs with the other hand, right? And when he threw a pass, the ball would spin in the opposite direction. Fumbles and dropped passes...