That's definitely true that in the studio it's processing the signal - but at home, tube amps are often doing the same thing. It is a form of distortion. Not all tube based systems distort this way, but I do see lots of listeners using underpowered amps for the speakers they have.
Tubes are a great way to emotionally get close to the music - I think of tubes as a way to create an illusion that performers are in the room with you - but I never think of this as accurate or neutral - but it can be very involving...
At home distortion is not the name of the game. Seriously. The ability of a tube amp to reproduce a more realistic soundstage (as depicted in your 2nd paragraph) is because they are better at low level detail which comes from the greater linearity that tubes offer. I've always been perplexed by the universal admission by both tube and transistor camps that tubes are inherently lower distortion, but then tubes are always getting docked for being 'distorted' simply because they sound better. The real reason they sound better is they have less of the distortions to which the ear is very sensitive (specifically higher ordered harmonics) although some designs may have more of the types to which the ear is not.
Many recordings are in fact made to present a true stereo image, which means a 3D soundstage with depth and Left-right extension, with everything in between.
20% of full power (I'm assuming that means average power) is a significant % but not outrageous if the speakers aren't crazy-sensitive. Am I to understand that SET owners go into it knowing they NEED to keep this contract if they want to enjoy their sound? If the "SET sounds a lot more dynamic" as it encroaches on this forbidden region, isn't it reasonable to think that SET owners (or dealers or wannabes) might poke through that limit just a wee bit to enjoy the subtle excitement of the extra dynamics? I need to hear this myself to know, but my guess is that doing such a thing might lead to one of those "wow, I never heard THAT before!" kind of moments.
I do see more people using speakers that are less efficient then the SET should really be used with, and they still enjoy the result. But its a simple fact that they are not getting nearly the performance out of their amplifier, simply because they are pushing it too hard. Most SETs don't employ feedback (this has a lot to do with the fact that you can't use feedback to extend bandwidth in a power amplifier, and if you are not really really careful with your timing constants in the feedback loop, the poor high end response of most SET OPTs will really get you in trouble- peaks before the roll-off, unstable operation, that sort of thing.
So since feedback is unwieldy and sounds wrong because it rarely can be applied properly in an SET, most designers don't do it. As a result, if you run it over 20% full power (on peaks, not average) the higher ordered harmonics will come into play, causing exaggerated dynamics and harsher sound. BTW once you know that distortion is responsible for a lot of the 'dynamic' quality of SETs, its easier to hear that it is in fact distortion doing it, so by reading this I may have ruined if for a lot of people. Sorry about that.
To take this a bit further, distortion is really a problem in all systems, not just SETs or tubes in general. As a result, I suspect that in about 90% of all audiophile conversations, the word 'dynamics' can be substituted with the word 'distortion' without altering the meaning of the conversation at all. For this reason I am careful to use a different word, like 'impact' when I want to talk about dynamic contrast. Too much unconscious stigma with the word 'dynamics'.