Question: Is all the emphasis on frequency response worthwhile? Certainly, frequency response is one of the most significant variables for audio quality (and one of the easiest to measure)...
Not easy to measure correctly -- if it was, everyone would be doing it. You MUST
have the right gear, the right test environment.
How relevant is it? Absolutely flat response is not essential, especially in the bass where room interactions dictate much. However, there is no substitute for a fundamentally smooth frequency response w/ no big anomalies. This, in combination with quickness, translates to a speaker that has the potential for real transparency. The first arrival signal from the speaker -- the direct path from spkr to ear -- is the one that "fixes" the core quality of the speaker. If that first arrival signal is not frequency linear, the results will be inconsistent.
Naturally, intelligent room-interactive design is essential, too. The idea of a speaker that you can place anywhere w/ equally good results is usually complete hype. The best designs always stipulate position, even room size/dimensions. It's the nature of room/speaker interactions.
EQ works in a PC desk speaker, but it always introduces phase distortion, which in a more transparent system become audible. And EQ cannot make fundamental fixes caused by design errors or shortcomings elsewhere. (simple example -- there is a dip at 200 Hz. Why? let's say it's because the xover is rolling the woofer upper response off quickly so its breakup modes won't affect the mids... and the chosen mid driver doesn't have enough power capacity there so its low roll off is also quick. You compensate by increasing gain at 200 Hz... which is OK unless/until the drivers are overloaded there -- and that will happen at a lot lower volume because of that additional boost.)
Good speakers are about consistently accurate/good results with a wide range of material and volumes -- flatter freq response definitely is an important part of this consistency.
Another huge issue is directivity -- A constant dispersion pattern over the entire frequency range -- that is the ideal, imo. If it varies a lot with frequency, results are inconsistent and not as convincing. Either dipole or omni is better than simple forward firing.
The most fundamental problem with 99% of conventional speakers is that they are omnidirectional in the bass, but much more directional higher up in frequency. 20~100 Hz tones fire in every direction almost regardless of bass driver/enclosure design, but by middle C (260Hz, center note on the piano), on most box speakers, it is usually not better than... maybe 3~6 dB down 45 degrees off axis, and at least -10 dB by the time you get to 90 deg. This varying polar radiation "excites" room resonances in different ways at different frequencies, and we human beings easily hear the discontinuities. It's one of the reasons that you can usually tell in seconds whether the music is live or canned.