Considering audio power amps, the input signal power is negligible, compared to the amp's output power. Consider a closed-loop voltage gain of maybe 10x to 50x, and you're also comparing an output load impedance of 4-8 Ohms to an actual input impedance in double digit kiloOhms at the very least (let's skip the debate about noise figure vs. signal source impedance for the moment). Thus, the power gain can be 10000x or above.
If you should mean an RF line amp, a fairly normal power gain of +20 dB still means 100x amplification. Does 1% difference in energy efficiency make any practical difference?
In that context, overall energy efficiency is a much more useful figure: power output vs. power consumption. Note that class AB linear amps have a typical efficiency of 50 to 65 % (71% theoretical maximum for a sinewave signal and DC power rails), "switch-mode" class D amps have "switch-mode" efficiency levels (80 to 90% or maybe more). The figures above are for "very little distortion", often specified as 1% THD. One particular aspect, where knowledge of energy efficiency of the circuit comes useful, is thermal design (heat dissipation).
=> it's rather a question of definition and practical utility.