"A higher impedance means more efficiency." Bullshit. It totally depends on what the amp is design for, there is no rule or law that says that a higher impedance is more efficient.
Though, lower impedance designs generally require more of the beefier parts, due to the amount of current the parts must handle as a whole. IE Larger SMPS transformers(More parallel runs of magnet wire compared to more turns), beefier output bridges to handle the current demanded from the low impedance load presented upon the SMPS. There comes a point where more current is desired over more voltage, given it is within part specs.