Almarg- OK, I see your point, but in practice such an amplifier will in fact 'produce an excessively bright response' not due to frequency response variation but due to generation of odd-ordered harmonics.
I apologize for repeating myself often, but the simple fact is that that audio industry is ignoring 45 years of research into how humans perceive sound! Were that research taken into account, I would agree that your statement is correct as today's amplifiers would be different. What amazes me about all this is how the audio industry has stuck steadfastly to design rules that, even while they were being implemented during the 1960s, were already being proven wrong by said research.
What I am talking about is the typical amplifier that you are describing violates the most fundamental rule of how we perceive volume, by exaggerating odd-ordered harmonics. Another way of putting this is that you can be convinced that a sound is a lot louder than it really is if the 5th, 7th and 9th harmonics are tampered with. These harmonics are not only cues to the human ear brain system, they also contribute to brightness- quite literally our ears are more sensitive to these harmonics than they are even to vocal frequencies! So there is almost no way an amplifier like that will not appear to have excessive highs.
This is the fundamental reason why tubes are still around after being declared 'obsolete'...