The flywheel, or flexplate, mounts to the engine's crankshaft and also serves as a mounting location for the torque converter. Consequently, the flywheel or flexplate transmits engine torque to the torque converter housing. The flywheel's ring gear also serves as an engagement point for the pinion of the starter motor when cranking the engine. Because of the lightweight design of the flywheel or flexplate, it does not help to smooth out power pulses from the engine like the flywheel does on a car with a manual transmission. On cars with automatic transmissions, the torque converter provides this function.
Automatic trannys technically do have clutches also, but not in the same sense as a manual transmission, therefore, the flywheel on an automatic tranny does not serve the same function as it does on a manual transmission, thereby making swapping it out with a lighter one useless.