Current amp vs Voltage amp

But as we saw in the ESL example, the model falls apart.

nah! your ESL example, I think, is a bad one. There are several SS amps manuf that have ESLs in mind & they do sound very good with ESLs. Yes, if you pair a SS amp not designed to take a high capacitative load then it will destructively fail immediately/over time. Your example assumes that one would take a SS amp not designed for high capacitative loads & pair it with an ESL & then complain about the sonics. Give both the manuf of ESL amps & the listener the benefit of doubt that they will be using an ESL amp for an ESL speaker & then compare tube vs. SS power amps for ESLs.
Maybe there is another example that you could cite where the voltage paradigm fails? Thanks.

Bombaywalla, actually that example is excellent. I have yet to hear a transistor amp that can play bass on a full range ESL, assuming the ESL is set up properly (at least 5 feet into the room).

Horns are of course another example with the only exception I know of being the Avantgarde Trio, which is (or was) designed for transistors. One of the reasons horns got a reputation for being 'honky' is the fact that a crossover designed for an amplifier with a high output impedance will not work right with an amp that has a low output impedance. As a result the horn is trying to play material that is out of its passband.

Full range single drivers are yet a third example. You will find that the users of such speakers are usually using a low power tube amp, usually one that has no feedback.

A 4th example is the very first acoustic suspension loudspeaker ever made, the original Acoustic Research AR-1. This speaker was designed for an amplifier with a 7-ohm output impedance, and would not play bass right with most solid state amps as a result. With such amps a simple solution was to put a resister in series with the output of the amp, simulating a higher output impedance.

I can also refer you to this:
http://paulspeltz.com/tomcik/index.html
This article shows that just simply having a high damping factor does not always do the trick. Some speakers want a 10:1 damping factor, and others want 0.1:1 (and yes you read that right- such a speaker might be designed for open baffle operation).

I did not make this stuff up BTW, it was well-known back in the 1950s when the industry was trying to sort out what to do about it. Tomcik, in his article above, proposed a solution that was also used by Fisher. Here is a google search on the Fisher A-80 amplifier:
https://www.google.com/search?client=ubuntu&channel=fs&q=fisher+A-80+amplifier&ie=utf-8&oe=utf-8

Take a look at the first hit. Its a YouTube image of a Fisher A-80 tube amp from the 1950s. Take a look at how the damping knob is labeled: "Constant Voltage" at fully counterclockwise, "Constant Power" at 12:00 and "Constant Current" at fully clockwise, where the amp is using current feedback.

I have to agree with Bombaywalla. Some manufacturers of ESL's specifically made/make ss amps for use with their speakers, Acustat and Sanders come to mind. Many ESL manufactures use ss amps when demonstrating their speakers. I remember a particularly fine demonstration of Martin Logan's with Threshold amps.

It does beg the question, why aren't more manufacturers making powered speakers, and why is it that people don't seem to buy them. Since the interface between speaker and amp is critical, and hopefully a designer has taken that interface into consideration in the design, it does seem logical that a powered speaker should be the best of both worlds. Ideas?

The problem with powered speakers is it eliminates any possible flexibility of choice.The asuumption that the builder will have selected the 'best' amp-speaker match is well,an assumption. If your hearing/listening bias differs from the builder you won`t be satisfied with this 'fixed pairing' and won`t be able to tailor to your preferences.This powered speaker could measure superbly on paper yet the possibility exists you may not care for the sound regardless.