Given that this is false what follows does not have univesal application....
I don't understand why you disagree. The ideal amplifier is a variable voltage source, and the ideal variable voltage source has zero output impedance.
Also, you state power supply current as the culprit of load impedance minimums, but this is an over simplification. The output stage is in between the power supply and the load. So is the speaker wire. Connectors too, but since you think damping factor isn't important....
Here's an easy experiment you can do to examine the effect of output impedance driving a speaker.... Run a simulation with an ideal voltage source through a resistor into a speaker load model. The parameters of the speaker model can be simple (let's say, a two way system). Run plots of the response across the source resistor. Step this resistor value using a range equivalent to a damping factor of 1 to 1000, log. Check out the "loss" across this resistor!
Keep in mind many speakers use drivers that have a HUGE impedance spike at resonance, typically 30-100Hz, which is where (freq wise) manufacturers typically measuring damping factor. This happens to be where it matters the least. Typical amps the start losing control of the speaker as the frequency rises, ironically as the speaker's impedance goes lower. Many well respected high end speakers go below 2 ohms, for example. So, that leads me to another question....Have you ever heard a Cherry Amp?
Specifically our newer models, like Maraschino or MEGAschino? These are good examples of what amps with high wideband damping factor, low distortion, DC coupling (no bass phase shift), high bandwidth, and low noise can sound like. Plus, we take it through additional steps to optimize for sonics. This is why Cherry Amps don't suffer from the "dry" sound of other Class-D designs or the "sloppy" sound of tube amps. Those are bold claims, yes, but I'm not alone in my opinion here. Take a look at reviews on our Circle. The proof is in the pudding.
When it comes to damping factor, there's no reason for wanting it lower. Well, maybe if your selling amps with poor damping factor.
I want you to know that I do appreciate your use of math and science. That is refreshing, and even if we don't agree on some narrow issues, we both believe in engineering.