That's not true. New designs have made AM transmitter much more efficient... it used to be that a 5 kw transmitter in the tube era would use about 10 to 12 kw hours of electricity. Today, it is more like 7 to 8 kw hours with enhanced modulation techniques and less AC and cooling. FM transmitters, too, are more efficient with solid state, but most of the difference is in the cost of cooling the transmitter and cooling the transmitter building when the weather is warm.
And with today's electricity costs, running any transmitter can be expensive. Think of it this way... transmitters are not 100% efficient. So the get one watt out, an AM transmitter and cooling may use up to 2 watts of power, and an FM today about a watt and a half.