Sometimes I wonder if 45s and 2A3s are more "soulful" because they are being driven into distortion much sooner and people love themselves some soft clipping.
I don't think so -- I actually don't much care for the "autocompression" sound of these DHTs as they approach nonlinearity -- they get hard and glassy sounding (to me). With ca. 104 dB/watt @ 1 meter sensitivity loudspeakers and my preferences in music and listening SPLs -- I think I am typically at output power levels on the order of 100 mW.
I also don't think it is the euphonious second order HD; that's a factor in gee-tar amps, but shouldn't be in hifi.
I do think it's because vacuum tube triodes, within their capabilities, are phenomenally linear amplifications. Transistors and tetrodes and pentodes... are not, and it takes a fair amount of EE skulduggery to make them behave linearly. My own opinion is it's those very tricks that tend to suck the life out of many (all but the best) amplifiers using those gizmos for power amplification.
Frankly (and, again, to be really explicit, IMO), for a given, relatively modest price point -- e.g., ca. $1000 -- it is going to be easier to find a great sounding, truly "musical" little stereo 2A3 power amp than a great sounding, truly "musical" amp using any of those other power amplifier components (SE or PP). Obviously, the comparison is never going to be apples to apples; the choice of optimal loudspeaker in either broad class of amplifiers is going to be quite different. Quite different.
All I can offer are my quasi-fact-based opinions; I don't have spectral data on harmonic content of a signal as a function of output power for the JE Labs "simple 2A3", to say nothing of having any such data for the slightly modified version thereof that I have playing NPR as I type this.