Why are there speakers designed with widely fluctuating impedances and steep phase angles in the first place?
A woofer in a box will have a resonance that is expressed as a peak in impedance. If there is no accommodation for this fact either in the amp or the speaker, the result will be too much energy at the impedance peak.
In the Voltage Paradigm the amplifier power is throttled back. This effectively insures flat frequency response. In the Power Paradigm the box design puts the peak at a lower frequency to take advantage of the extra energy- but again netting fairly flat frequency response, but wiht the additional benefit of bass extension, which might well be up to half an octave.
Some speakers don't have impedance curves based on box resonance. With such speakers, the Voltage model falls apart. A good example is an ESL, whose impedance curve is based on a capacitor. It really works a lot better if the amp makes constant power rather than constant voltage. That way the amp can make power in the bass regions where the impedance is high. This is why transistor amps tend to be bright and bass shy on ESLs- and typically why owners of ESLs and transistors put the speaker too close to the rear wall, to get bass reinforcement. They are not realizing the full potential of the speaker.
Anytime a Voltage Paradigm product is used with a Power Paradigm product, a tonal aberration will occur. We audiophiles call that 'equipment matching'.
One could also ask why amp designers choose not to build amps that can deal with such loads?
(This question is posed in the context of 'difficult' loads with low impedance or high phase angles)
The answer here is quite simply, such amps that can drive such loads are usually incapable of sounding like real music, as they have design features that violate human hearing/perceptual rules. One common example is the application of negative feedback, which, due to propagation delays in the amplifier circuit, causes ringing distortion, typically odd ordered harmonics (5th, 7th and 9th) which are used by the ear to sort out how loud a sound is. This is a pretty fundamental hearing rule. Amps that violate it have the coloration of brightness and also come off as harsh.
If you want to get away from that you have to figure out how to make a low distortion amp that uses no feedback. As stated earlier, distortion often take precedence over actual frequency response errors by the human ear, IOW its more important to have low distortion than it is to have perfectly flat frequency response (which can't be counted on in the best of circumstances anyway).