That's a reasonably insightful post John. I'm well aware of the basic elements of amp engineering and I consider myself lucky that I have been able to turn to such an esteemed amp engineer as Tom Cumberland to patiently answer my sceptical questions over the last few months. I absolutely agree that flat frequency response and inaudibly low distortion are indeed the hallmarks of any good solid state amplifier. Let's set aside tube amplifiers for a moment since their relatively plentiful 2nd order harmonic distortion can make for an audibly pleasant difference in sound compared to a solid state amp.
Another distinguishing audible factor does indeed have to do with what many people including myself generically call "speed" and encompasses several time domain factors influencing sound. A few worth noting are damping factor, slew rate, size and number of the array of capacitors and how they are aligned, bridged or unbridged amp modules, size of voltage rails. Designers have many, many variables to ponder and integrate, all of which can be utilized to be completely neutral or impart other sutle sonic qualities.
The ability of the amp to respond to an input sigal does vary depending on the its own design attribute and the load presented to the amp by the speakers/cables. To me those attributes are most audible in the bass region, hence you hear people describe the certain amps as sounding "fast" compared to other amps. Other people may be more sensitive to higher frequency sounds which some people refer as "brighter" sounding or sometimes having a solid state "edginess". To be more accurate that phenomenon should really describe the amp/speaker interaction. But by not changing anything else in the system except the amp one should be able to detect an audible difference if any between amps having somewhat different designs and specs.
In the case of the a-1400-a, I know from long discussions with Tom and Ian how highly they regard the Bryston amps, a long time favourite of mine. One reason this product took so long was they're determination to come out with an amp being the sonic equivalent of a stack of the longtime Bryston flagship 7B monoblocks. Knowing the stereo version of this amp well, the 14BSST, from owning it for a whileI was very sceptical as I mentioned at the start of this thread. Bryston amps are one of the most highly regarded amps and legendary for their bass control and...I have to use the description...speed.
You make an arm waving point about the importance of adhereing to basic principles of engineering. Its been 3 decades since I studied engineering science so forgive me if I'm rusty but I must tell you that those lofty principles, whatever that means, often don't hold up under real world conditions which is why its a science that continues to grow and evolve. The latest apparent contradiction which I am still trying to reconcile is why I hear an improvement in sound quality in a typical HT from using dual centres such as the VP150 when all the "principles" suggest the sound should be compromised due to lobing. Too many other variables must be coming into play.
With respect to the article you cited he contradicts himself in the middle of the second paragraph but I understand his general position which I have moved away from over the last 20 years. Here is a more technical article on high voltage amplifiers which goes into more detail on some amp design parameters. The main point to glean from that article is not the technical detail but to show that the skilled amp engineer has many ways to influence how the amp processes the signal and therefore can affect the sonic quality of amplified output. I am not saying that every SS amp will have a different sound. But I can say strongly that the Axiom amp bears a very close sonic signature to the Bryston amps which inspired its design.
http://www.falco-systems.com/high_voltage_amplifiers.html 
