Ja, the wisdom of the past ;-) replicated over and over, now B&K again. What about a breakthrough?
Connecting to the past: "with music ...". With music or any noise to speak of, the spectrum comprises harmonics in itself. Question is, if the harmonics additionally generated by the speaker for instance, contribute so much, that the overall impression changes.
So, how are the harmonics in music distributed (spectrum)? Bassguitar, played 'clean': 400% (!!!) second, 100% (!!) third harmonic plus lots of higher components. How far would like 10% of HD from the bass-speaker distract the listener? Especially as the spectral content of the instrument depends strongly on how the chords are picked by the musician ... . Another is, again 'clean', the electric organ with just 50% 2nd, 10% 3rd, and little higher components.
More crucial is intermodulation, that originates in the same non-linearities. But worse, because in regular musical presentations, the instruments generate their own spectrum, and do not interfere with each other. But a wideband speaker logically would generate IM from a bass tone combined with all the sweet 'female voices', reproduced at the same time. These IM come not natural to the music. They distract as an additional phenomenon in the sound field. Ony that people got used to it. So much so, that a clean speaker sounds 'thin', 'clinical', what have You. The thickening, the muddiness, maybe even heft became a quality parameter in its own right, a matter of taste. How much speaker sound do You prefer?
Plus, IM can be generated not only in the motor. A very prominent source is the surround of bass/midrange speakers. It may raise the IM of an otherwise o/k-ish speaker to 30% with just 3mm of an excursion. (That's why the Purify's surround looks that weird.)
Thing is: tja, what is it? Breakthrough needed, me thinks. Discard the two-way concept for starters. Quality begins with a four-way, may it be with a 5" bass ... especially with smaller basses because of the high excursion needed ... the cheapskates we are ;-)