Hi All,
Oboy . . . this is opening a subjective can of worms. I'll try to be as objective as possible, but I'm apologizing in advance if/when I piss someone off.
The pentode 1st amp/triode cathodyne phase splitter was developed to produce the most bang for the buck. Cathodynes need lots of gain to work properly, and a pentode stage preceeding it was one of those "duh" decisions. Heath was one of the first companies to use the configuration in 1958 with their W7, which used a TV IF amplifier/sync separator tube, a 6AN8, to perform the duty. Dynaco, and others, followed suit, and the "three tube" power amplifier was an accepted member of the hi-fi scene.
The most notable characteristic of the above circuitry, in my rather extensive listening experience, is that it is euphonic, but inaccurate. The midrange is somewhat "forward" sounding, with all the "tube" overtones, but there is a nebulous characteristic that prevents (or inhibits) the detection of individual instruments. I have referred to this phenomenon in the past as sonic soup.
Triode stages, and the long tail phase inverter in particular, have a more neutral sound that requires a little more dedicated listening to appreciate. The midrange is apparently more subdued, but it's actually because the low and high frequencies are more accurately represented. I call this sonic salad.
In designing amplifiers professionally, one has to subject oneself to listening to the same program material over and over and OVER and OVER in order to detect the subtle change a different cathode resistor or feedback capacitor value makes. It also takes a listening discipline that most DIYers (and virtually all audiophools) aren't willing to invest the time or effort to subscribe to. There's nothing wrong with that; if it sounds good, listen to it. But if you do decide to learn the discipline, you'll be rewarded (and cursed) with hearing, and recognizing things you never heard before.