Agreed years ago used to do it myself, but not to test an Amplifiers’s protection. Not arguing over the validity of using Square-Wave testing providing it’s pertinent.
I have not been following this closely since it seems to have devolved into some sort of debate/pissing contest. As stated above, a square wave test into 8 ohms in parallel with 2 uF used to be a pretty standard test representing the load many speakers presented to the amplifier. The Quad ESLs shorted the input terminals (i.e. amplifier's output terminals) when overloaded. I would like to know my amplifier would survive if not thrive driving whatever speakers I have, and that means looking at the resistive and reactive components of the load. Ported speakers tend to have impedance minima around the port tuning frequency when the woofers are essentially static so a DC impedance. Through the rest of the band the impedance often varies widely (I often use the term "wildly") due to driver/crossover interaction. It all makes for a fairly complex load that the amplifier sees, and square-wave (step-response) testing is a long-used method in simulations and the real world for assessing the broadband performance of an amplifier. I am not sure exactly your issue with this.
How would you calculate damping factor using an Electrostatic load? An Electrostatic panel is a reactive load with a leading power factor. The opposite of the load presented by a conventional speaker.
Damping factor in this audio world (vs. the control world where it is a term in the denominator of the impulse response equation) is DF = Zload/Zsource. Z (impedance) is in general complex and depends upon frequency. Most discussions and spec sheets only provide the magnitude and often at just one frequency, sometimes a few (LF, MF, HF). If you just calculate magnitude, as is typical (and what I clearly stated in my opening posts), then phase angle affects the magnitude (since it changes the real and imaginary components of the impedances) of the speaker and the amp (and cables between them, natch). The calculation does not change, but speaker and amplifier impedance most certainly do, thus damping factor varies over frequency. Personally I prefer to look at impedances but that's the way I was weaned. Damping factor, like a single SINAD number, hides too much information.