Let's assume we have a single dynamic cone speaker with a pass band of 35Hz to 20K Hz. Let's forget about high frequency beaming and cone breakup. Just assume this hypothetical speaker has a flat frequency response within its pass band, as measure on axis.
Bifwynne, I agree with Ngjockey here that if your hypothetical speaker has a flat freq response between 35Hz & 20KHz then all signals in this frequency region will pass thru minimally unaltered. That's the meaning of "pass band" - frequency passes thru minmimally altered. This, of course, means that in the 35Hz-20KHz the effect of the speaker coil moving inside the magnetic field poses no issues. So, there should be almost zero phase shift in the 35Hz-20KHz region.
Is there a frequency range where a speaker is phase coherent
yes, its phase coherent inside its pass-band. In the case of your hypothetical speaker it's phase coherent within 35Hz - 20KHz.
or does phase nonlinearity increase as a function of frequency ... period??
yes, it does. And, in the case of your hypothetical speaker, phase coherency degrades below 35Hz & above 20KHz both of which are outside the pass-band of the speaker/driver.
If the answers to all of these questions are -- yes, then it seems to me using 1st order X-overs and sloped baffles is at best a rough justice engineering response to a problem that is inherent with dynamic speakers that use voice coils.
Bifwynne, I'm not sure that you realize what the benefit is of using 1st-order x-over? The benefit of 1st-order x-over is that the PHASE DIFFERENCE (not talking about the absolute phase of a certain frequency) among all the signals in the audio band (20Hz-20KHz) is constant.
So, you have a music signal coming into the speaker. This music signal is a complex mixture of many frequencies. All these frequencies have some absolute phase that is different from each other. Further, each frequency has some non-zero phase difference with another frequency in this complex music signal. So, this whole complex music signal now goes into a time-coherent speaker as an electrical signal & comes out as a sound pressure wave. The phase difference amongst all the frequencies in this complex music signal do not change (i.e. remain the same) if the speaker used a 1st-order x-over. This means that the timbre & harmonic structure of the music remained unchanged as it passed thru the speaker. No other higher order x-over can achieve this i.e. higher order x-overs change the phase diference among the many frequencies of the music signal as it (music signal) passes thru these higher order x-overs.
So, ifffffff, the solution is a moving target (as you wrote) a time-coherent, first-order x-over speaker is the least damaging (IOW, the best compromise solution to a moving target problem).
hope that this helps some.....