Or is this an audiophile myth?
The honest answer is yes, but no one can tell which amps and which speakers.
The amp loudspeaker interface is very complex, little understood and not studied nearly enough.
Amps are bench tested into purely resistive loads, which are far removed from real world conditions.
There are some generalizations. If you are daft enough to side with the tubes are better brigade, then you do have a much more limited choice of speakers. Tube amps are upset much more by complex loads than solid state ones.
I think for most two way speakers this is likely a non issue.
The problem comes with exotic three way speakers, that have passive crossovers at too low a frequency. These speakers frequently have complex phase angles and worse drop the impedance below the DC resistance of the drivers. That in itself is a contender for a bad speaker period.
We are now at the point were any decent three way with a low crossover point should be an active speaker to be in any contention to be state of the art.
The issue comes that high priced amps you could use as arc welders are more likely to cope with these aberrations than cheaper amps.
Electrostatic loudspeakers present a special case, as they have to tolerate high capacitance across the load which can send some amps into supersonic oscillation, and blow them up.
Actually few designers have really focused on designing their amps to perform optimally with a wide variety of loads. The late Peter Walker and founder of QUAD Electroacoustics was one of the few who obsessed about this. Part of the reason for this, is that he produced electrostatic loudspeakers that have become icons.
