I agree with you that frequency response is the most important feature in the reproduction of the illusion of accuracy. I think it's closely followed by distortion and the other issues follow those two. Frequency response is where things like overdamped and underdamped filters will show up. Distortion - particularly in the midbass through the midrange - makes the sound fatiguing and less clear. Other reproduction imperfections are worth making an effort to improve, but the "must have" considerations are flat response and low distortion.Both of these are things that can be improved by techniques like you've described. The octave below 40Hz is a challenge for high-efficiency speakers. Basshorns tuned for use below 40Hz are very large. Direct-radiators tuned for high-efficiency either lack extension or they're large too. That means you usually have to throw power at the problem. You can bump up the EQ or add subsystems or both. You can tune a cabinet so performance in the bottom octave is optimized, which is really an acoustic EQ. All of these are ways to get more power available for the bottom octave.
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