I was refering to Al's post, you posted between. I'm not overly convinced you actually hear the box itself (it would be to be pretty awful for that to happen). And resonances can be controlled, so I'm not all in on the idea that inertness inherently is the most advantageous thing always. Consider that ports are resonating devices... and a lot of people like old Altec speakers where if you make the box really inert then people don't like them as much... There are a lot of things going on with that, and it's not as simple as one might think. Consider that boxes aren't springs, for one.
I would say the speakers that sound the most like a given character are typically sealed, super inert boxes. They don't sound bad, but there is a flavor to them IMO. There's nothing to dampen it because highly damped drivers don't work in sealed boxes. But if the box wasn't as inert it might dampen some of it. The trick is understanding what frequencies are doing what, and controlling it. It's a case by case thing between speakers - obviously there can be horrifically bad loosey boxes, too.
On my speaker prototypes I actually had to change a brace because it robbed the midrange severely. You can get cancellation issues if the box resonance isn't far enough in one direction, or is in the wrong place. So maybe I could brace my way out of it, but in a prototype it isn't worth the trouble and the losses are pretty negligible.
Inertness of a box doesn't remove resonances, but it does move them up in frequency. Mass moves them down, stiffness moves them up... Stiffness typically will end up dominating. Is that the best way to arrange excess energy, turning it into really high frequencies? or does it makes some kind of sense to reduce the vibrations? It's an interesting question, and obviously different manufacturers have different approaches.
What I generally think though is the electronics are more likely to give you the impression of a particular speaker enclosure, than the speaker itself. Swapping electronics can often completely change how much sound appears like it's coming from inside a speaker or is just around it and there's no way to tell it came from it - so I'm not overly quick on the draw to blame speakers all the time.