That's the point: when you take the same basic design and improve it with less distortion at the same power, it sounds better
Usually, at the same amount of distortion, this new design will have more power.
I have already said that I once would have agreed with you, because according to the specifications of TT, there is no way this kind of distortion would be heard at normal listening levels with HD 800 S.
Then I compared it to DAVE and heard that at the same level, TT sounds distorted (it's subtle, 1 in 50 tracks where you'd notice), simply because it is being played loudly. Turn TT down a little and the distortion disappears. DAVE didn't show this distortion, even when I played the music more loudly.
The specification for power is for a given amount of distortion. So two amps that can both deliver the same power will not necessarily have the same distortion when delivering that power. The amp with the worst distortion at the same power level will tend to sound worse.
As I say, I used to have the same point of view as you, that for "normal listening" SPL, headphones like HD 800 S aren't fussy if the amp is more than powerful enough, like TT. But it turns out that the distortion levels for headphone amplification specification are too generous... It's subtle, but I think it's unfair to suggest that more power (or less distortion at the same power) makes no difference.
TT and Mojo are about the same power for the same amount of distortion and so with headphones like HD 800 S there will be some pieces of music at normal listening levels where distortion will be heard, varying with volume level. Upgrading to DAVE (or perhaps Hugo 2, which also has lower distortion, I believe) will not show the same variation in distortion at these volume levels.