If I have to pick the most important factor in sounding live it's linearity. Double the input then the output should double. Triple and etc. And it's true in the entire system, not just speakers. I recall Bud Fried's speakers were linear phase and roughly time aligned but it was their linear changes in sound pressure level that made the sound real. And There are non linear phase and non time aligned speakers that sound real like ATCs and again it's linearity that makes it happen.
Why stop there? (one should be able to rank them maybe using Floyd's book)
But I think I agree with you, as non linear systems have a lot of harmonic distortion and IMD.
We can talk about the frequency response as the thing the translates best statistically to "being perceived as being good".
So if one had a speaker that was not time/phase correct, but had good frequency response, no cabinet resonances, and a good pattern, then they would sound better than a time/phase aligned speaker with bad FR.
If one uses a DSP to make the FR good, then we get a different fight.
If one uses a different DSP to also do impulse response (phase) EQ, then it is different again.
However a DSP cannot remove cabinet resonances , harmonic distortion, IMD, and port noise, and compression.
If you got ^those^ good however, one could do the rest in the specific few DSPs that allow it.
