How are LEDs considered efficient?
You seem to be getting confused between the efficiency of the LED and the efficiency of the circuit to drive the LED.

In terms of light output per unit of energy used by the LED they are an efficient way to generate light. In absolute terms they aren't great, they are around 10%[1] efficient in that respect however that is still far better than the ~1-2% of a conventional incandescent bulb.

But what of that power wasted in the resistor. A series resistor is the simplest way to drive an LED, it is far from the only way to do so.

Even sticking to a resistor what if we put 20 of your 2V LEDs in series and supply it with 45V? Now you are using 45*0.02 = 900mW of which 800mW is going into the LEDs and only 100mW (11%) is being used by the series resistor. 

But we can make it even more efficient, the reason for the resistor is that the LEDs needs a constant current and most electronics are designed to supply a constant voltage. The easiest way to convert from one to the other (assuming a constant load) is to throw in a series resistor.

You can get constant current power supplies. If you use one of those to drive your LED then the resistor can be eliminated and you can get an efficiency of well over 90% of your total system power going into the LEDs.

For a home project or a simple indicator on a signal a resistor is a lot cheaper and simpler but if you are driving a lot of LEDs then the logical choice is to pay a bit more, have a slightly more complex circuit and use a dedicated constant current LED driver IC. 


As noted in comments, 10% is a good ballpark for current household lighting and probably also about correct for cheap commodity LEDs using older processes. Newer single colour parts can achieve significantly higher levels of efficiency.