The basics jive with what I think I know, and in terms of general application, for the general consumer, I think it is good information. In terms of impedance, I think anybody with a DATS or other method of generating an impedance sweep has probably already figured that out (or should have), and can easily confirm it.
However, that being said, not to misconstrue what you are saying, but if somebody got the impression that impedance doesn't matter, I think that would be incorrect. While it may be outside of general purpose application and mainstream use cases and performance requirements, some amps are impedance sensitive in terms of how well they perform, not just in terms of overheating, shutting down, or blowing up output devices.
Also, I don't know that the suggestion is a bad one, because I don't know how any given AVR is actually implementing the output 'limits', but if they were doing it by switching the output tap on the mains AC power supply transformer, that would hypothetically increase the current delivery capability of that portion of the power supply, which hypothetically could be of some use if the power supply was otherwise dropping voltage sag on the recharge cycle because of that limitation. Again, I don't know, but it would be nice to see detailed data on that, i.e., multiple measurements across variations of impedance (down to maybe 2 ohms) and frequency, and that data might be specifically relevant to a given model, depending on the specifics of the implementation of the limiting method, the power supply capabilities, etc.
The point that content is not a continuous test signal is a good one, and valid, though the degree of difference will depend on THE CONTENT, and the advantages of this as far as lowering prolonged current demand will similarly vary depending on the interaction of the content, the amplifier, and the loudspeaker. I.e., if you had something running a 10 Hz square wave at a high level (like EOT famously), into a loudspeaker impedance that was low at 10 and 30 hz, the larges frequency components of that signal, that could continuously be WORSE than equivalent pink noise peak voltage or continuous single sine wave signal, if it is bother larger in actual RMS value than the peak voltage would imply, compared to a nominal voltage noise signal or continuous sine wave, and with many loudspeakers might be dumping of pile of voltage into an impedance that just sucks up current on the best of days.