Why is the efficiency of this LED driver circuit so low?
This led driver is capable of low losses .The internal switching scheme is good in this respect .The internal N chan fet should be cool.The buck coil does have significant ripple current .This means that the magnetic field strength is moving up and down with the switching frequency .Converters of this family benefit greatly from a high Q inducter .Remember the relationship between Q and the ratio of energy stored to energy dissipated .Get the best coil that money can buy .There are still some switching losses so using more inductance will reduce the switching frequency and reduce losses .This means a bigger coil .The coil current has lots of ripple so on your diagram so does the led .The led does have dynamic resistance .You can ballpark the dynamic resistance of your led from the led data .Place a low esr cap like say a ceramic across the led .This cap will mean that the led gets smooth DC so its resistance will be less lossey.The cap should have a impedance that is much lower than the led dynamic resistance at the switching frequency .When I did this on a S trap buck I nailed things with a 10 microfarad 50V ceramic smd cap .I was running a 6 led white string .Your cap will be different         .Also look at the input cap .All buck converters take current in lumpy pulses .Low Esr will help you here .The freewheel diode is a significant loss contributer here because the output volts are so low .Shottkey diodes with higher current ratings and lower voltage ratings will waste less volts .