Which I guess leaves the question why does the input stage have the topology it does. The quick-and-easy approach would be a Mullard-style long-tailed pair or differential stage, or maybe borrow from Williamson or Dynaco and direct couple a half-6SN7 input tube to a "concertina" or split-load inverter. It would certainly be cheaper, and is the approach of just about every Golden Age amplifier.
This is the intuition part. There is something wrong with the sound of Golden Age amplifiers ... hard to describe, and it’s not there in SE amps. Something to do with diminished low-level detail, subtly flattened tonality, and a lack of air and "shimmer". The folks at Sound Practices were confident that this "PP" coloration was inherent in push-pull itself, and that’s where I parted company with the common wisdom.
I became convinced the problem was the phase-splitter tube. For one thing, the three approaches to vacuum tube phase splitting (split-load inverter, long-tail pair, floating paraphase) sound quite different, and they all have varying levels of that "push-pull sound". So why not take a passive approach? Studio transformers have been around a long time, and if they are good enough, retain phase integrity through 20 kHz. Then the rest of the amplifier can simply be fully balanced, with none of the circuitry devoted to phase splitting, just amplification. Do one thing, and do it well.
Sure enough, even in the first version of the Amity in 1996, the coloration was gone. It didn’t sound push-pull, and it didn’t sound SE, either. It sounded like itself, and not like anything else. The rest of triode community went their own way, off in SE-land, and I did a lot of historical research for Glass Audio and Vacuum Tube Valley, while thinking of the next steps beyond the 2-stage Amity amplifier.