One of the issues not discussed in audio is what happens with power amps using unregulated supplies and what happens to transistors when the supply voltage varies.
If we note the data books for transistors we find a gain bandwdth spec for a certain voltage actross the transistor, if the supply voltage chages then the gain bandwidth changes. Assuming that is the case then we have a feedback loop which is set for a certain gain bandwidth trying to hit a moving target, becasue the supply rails are moving up and down depending on load and the gainbandwidth is changing on the transistors.
So if all the above is true and the feedback loop is trying to hit a moving target, then I would expect variations over power and frequency.
Just to add a bit more to mix; when an amplifier is driving a reactive load the voltage and current are out of phase in the output drivers of the amp. If we are using a voltage feedback loop, as we usually do, then we have just exacerbated the problem stated above due to the reactive load.
I also suspect that if bias current through the outputs is for some reason getting lower under higher power conditions then this may also add to the problem.
Are we having fun yet?
d.b.