Indicator LEDs are about 2mA at 2VDV, so at 120VAC the losses in the transformer and rectifiers are far more than the power actually drawn by the LED. A neon lamp might actually be more efficient to run off of AC since you don't have all the losses of the magnetics. You could run an LED off low voltage AC and it would just illuminate on half of each cycle (some cyclists do this when they connect an LED directly to their dynamo without using a rectifier).