I've often thought of woofer speed not as acceleration but deceleration. The ability to stop fast is also speed and it affects the following tones since if it hasn't stopped it partly obscures the next tones and it reduces the dynamics since the next tones start from a higher noise floor. Basically it's the Q of the bass design that describes woofer control with 0.5 Q being maximal damping and 0.707 Q being flattest response. Above 0,707 the bass becomes more and more bloated. I might add that below 0.5 the bass becomes thinner and rolls off too quickly. There's more to balancing Q and bass cut off but that's a longer tale.
There is no substitute for cubic inch or in this case surface area
After listening to quite a few speakers, my conclusion is that if you want large enveloping soundstage, you need a lot of drivers.
I once had a speaker with two 12in. drivers and the soundstage is just floating in the air. None of my other speakers could do that.
Currently I have a pair of Thiel CS2.4. It is a very good speaker but with small drivers there is really limitation to what it can do in term of soundstage size. I really miss that.