I personally believe the power response is far more important than the on-axis response. The measured on-axis response only happens at a single point in space. The farther back your listening location, the more and more the power response dominates the perceived timbre. From about 5 feet on back, most of the sound that reaches your ears is reverberant sound.
In my opinion, good power response matters for two reasons: First, the ear derives timbre not only from the first arrival sound, but also from the reverberant sound. Live instruments give you a natural-sounding reverberant field, but very few loudspeakers do. One test is, walk out of the room and listen through the open doorway, with no line-of-sight to the speakers. If they still sound like live music from the next room, they're getting the reverberant field right.
The second reason getting the power response right matters in my opinion is, I have come to believe that the ear/brain system finds a significant spectral discrepancy between the first-arrival and reverberant sound to be fatiguing over time. I can go into more detail about this if you'd like.
Loudspeakers that do a good job with the power response include Maggies, SoundLabs, Gradient Revolution, Altec Model 14 and Model 19, JBL Model 4430, BBC-spec LS-3/5a, MBL Radialstrahler 101e, ESP, Mirage M-1 and M-2 and recent Omnispheres, Shahinians Obelisk and up, GedLee Summa, large Tannoys, corner horns by Klipsh or PiSpeakers or Classic Audio Reproductions (Hartsfield), Allison Acoustics, SP Tech, Linkwitz Orion, and my own Stormbringers and Jazz Modules. I'm sure there are many others that I can't think of offhand. As you can see, good power response can be accomplished with planars, direct radiators, and horns (or waveguides).
Duke