Jerry
It is just about good practice. On AC the LED is doing double duty as it is also serving as a rectifier blocking the reverse polarity that is not used. This may or may not shorten the life of the LED,it depends on the design. As mentioned to achieve maximum intensity a bridge rectifier will use both halves of the sine wave and an added capacitor will achieve steady current. In fact if a capacitor is used even with the single diode maximum intensity will also be reached as the half wave will charge to peak assuming the capacitance is sufficiently large. Using the bridge is the most efficient method. No matter how it is run the LED itself is a DC device.
Being that a diode costs about 2 cents,it is not a bad idea to include it.
Dale H
