Resonances, both from the driver and the cabinet, have been shown to be detrimental to perceived sound quality in numerous perceptual studies. There is one study in specific which summarizes a majority of the previous work as well as repeating these studies and expanding on them:
Toole, E. Floyd.
The Modification of Timbre by Resonances: Perception and Measurement. JAES Volume 36 Issue 3 pp. 122-142; March 1988.
As far as audibility is concerned this has been shown to be related to a few factors:
Q of the resonance - High Q resonance is less audible than low Q resonance.
Frequency resonance occurs - Hearing sensitivity varies with frequency. Due to this there are some frequencies where, in certain situations, resonance can be heard even if it is attenuated [relative to playback level] by about 20dB in other cases the resonance can be above the playback level and still be inaudible.
Source material - Different types of recordings or test tones are more or less revealing of resonances. For example, typical pop music will be far less revealing of resonances than a piano solo.
Acoustic environment - Reflections have been shown to increase audibility of resonances [both from the speaker, bad, and the source, good]. So listening to headphones will be less revealing of resonance than listening to a pair of loudspeakers in a typical room.
The article I mentioned goes into specific circumstances for audibility of each of these issues.
So, why is resonance still such a problem and why does its coloration not show up in typical frequency response graphs?
Typical bracing techniques do not attenuate resonance such that it is no longer audible, but at the same time, common measurement techniques do not capture the coloration due to resonances. To properly measure resonance one would have to take multiple far field impulse response measurements at varying angles in an anechoic chamber then using these plots derive a waterfall that would actually show resonances. Now, this is fairly unreasonable to do, so a more simple, less accurate method, would be using an accelerometer attached to the speakers cabinet at various points to at least get an idea of what resonance it does have.
Take, for example, the Primus 360 an all around superb speaker, but it uses typical bracing techniques and has a fairly large radiating surface area [cabinet]:
Please note that Stereophile does not take into account loudspeaker sensitivity when measuring resonance. So, if comparing a loudspeaker with sensitivity 93dB 2.83v/m such as the 360 to a loudspeaker with sensitivity of 90dB 2.83v/m as the 802D the resonance plot of the Primus 360 would need to be dropped 3dB to be compatible to the 802D. Because of this I will note all compared sensitivities above the graph.
[93dB 2.83v/m]
These resonances are not just audible, but would be extremely detrimental to sound quality for nearly all types of source material
The Revel Studio2 [88dB 2.83v/m]:
Not only does this unit is far more extensive bracing than typical, it also uses thicker walls [fairly inefficient, but better than nothing]. As seen, these resonances are far lower than is common in most loudspeakers, but will occasionally be audibly with the right source material.
B&W 802D [90dB 2.83v/m]:
This unit uses an extremely complex bracing matrix as well as a specialized mid range enclosure that is absolutely inert. No audible resonances would be observed. Please note that there must have been some other vibration creating the peak centered at about 50Hz as it is not physically possible for this unit to resonant at this frequency with its internal structure.
Also, while the measurements Stereophile provides are useful, there analysis of them is plainly put, a joke. There is no actual correlation of the resonances to perceptual research, as far as I can tell, but rather if it looks 'good enough', it is or isn't audible depending on the situation.
In the end, with current technology it simply is not feasible for large scale production of inert cabinets to be made while retaining a low market price.