To state that the nonlinear aspects of speaker performance are "minimal" is, in my opinion, a subjective determination. (And my opinion is also subjective.)
That's fine, but I do not consider those nonlinearities to be "minimal" when it can be easily demonstrated that simply changing a single speaker for another one that fits in the same cabinet can have a dramatic effect on the sound. Such an obvious difference can not be "minimal".
My Axe-FX setup is simple: AFII to Alesis stereo power amp (RA-100), to Hartke 4x12 angled cab loaded with Celestion G12M25 reissue Greenbacks, well broken in. I make two assumptions which I believe are reasonable: 1: That the output drive stage of the AFII is linear in its behavior, so that the signal delivered to the power amplifier varies only in total level and harmonic distortion content does not appreciably change over its full range of output. 2: That the power amplifier is also very linear until it reaches its rated power output of 75 WPC into a nominal 8 ohm load, or 100 WPC into a nominal 4 ohm load.
So, working on the belief that these assumptions are accurate, then whether the system is driving the 4x12 at subaudible levels, or at "speakers will die shortly, right after eardrums" levels, there will be no variance across that range, with regard to the harmonic content going to the speakers.
Yet, there really is no doubt that the speakers sound different when being pushed pretty hard. There are audible cone harmonics that only come out when it gets loud. I can hear them clearly even when using earplugs and earmuffs for double hearing protection.
Those cone harmonics are probably still there at lower total volume levels, but they are at a lower level relative to the total output. Their behavior is less linear at higher output levels.
With the amount of DSP power now available, I predict that it's only a matter of someone taking the time to create a system that more accurately models speaker behavior than the current IR model, which reflects speaker behavior very well but only at the one volume level it was measured at.
Since Fractal Audio is unquestionably the leader in DSP amplifier modelling, it stands to reason that the brains behind these wonderful products should hopefully be interested in pushing the modelling of the speaker system to new heights of performance as well. And that will require a more detailed approach to modelling the full-range dynamic performance of the speaker system.
Beat the competition to the punch. Create a multi-dimensional IR capture and playback methodology that captures the speaker performance at a range of output levels which will capture how it responds differently at those various levels.
Eventually, somebody's going to do it. Might as well be Fractal to get there first.