I've heard many SETs. What you are saying (without knowing me, but if we give your comment the benefit of the doubt) suggests that most SETs are junk
You are incorrect about the 1st Watt thing and the larger odd harmonics. The issue is topology; some PP amps may well have the problem you describe, but most don't. They have a different problem, where single-ended and PP circuits are combined in the same amp, which results in both a
quadratic non-linearity and a cubic non-linearity, resulting in a prominent 5th harmonic (which is similar but not the same as you describe). That can be avoided with careful design. BTW I'm not saying the 1st Watt isn't important- everyone knows it is. What I am saying is a PP amp can have a 1st Watt better than any SET.
The other apples and oranges (not on an even playing field) have to do with improperly applied negative feedback, which results in a greater amount of higher ordered harmonics (similar to what you might be describing, as that doesn't sound very good) and the class of operation (AB instead of A1).
So often when an SET is compared to a PP amp, the PP amp usually has these three problems thus described.
So to even the playing field, the PP amp needs to have the same class of operation and no feedback, as well as either the same output power at clipping or the same power tubes as the SET (take your pick). I've found though that if you apply feedback properly it does not hurt the 1st Watt at all.
Now what an SET can do that most PP amps with feedback cannot is have a ruler flat distortion vs frequency curve across the audio band. I can get into the engineering about how this is so (and probably did earlier on this thread). Its one of the more salient reasons amps can sound amusical. But you can have a PP amp do that just as well if you know what you're doing.