The vast majority of speaker cabinets are fairly cheap six-sided boxes with a fair amount of resonance as part the sound signature. Eliminating resonance and flex is certainly beneficial, and should be a considered a step in the right direction in the pursuit of ultimate performance. It should improve dynamics and reduce coloration through the most critical lower to upper midrange. Lack of vibration from the cabinet can even help improve treble clarity.
The question is how much of an audible difference does it make...that’s a variable influenced by the rest of the speaker, the room and rest of the system. If all else is equal and you substituted a poor cabinet with a really good one, it should be audible, but it’s only one contributor of the many aspects that influence the overall sound. There are a lot of things that a high end company will do to improve sound of their products that many large conglomerate corporate mid-fi companies won’t bother with due to added cost with minimal marketing returns....my guess is that they (and maybe their followers) will argue that it doesn’t make a difference. If you make every effort, things can reallly add up for an improvement. If you make enough decisions not to bother for the sake of more profit...you have a mediocre product (even if it’s well marketed)....and that is often what separates mid-fi from high end.

