A few basic points are missing from this discussion (although admittedly i did not spell each msg).
1.
Damping Factor is only in play when each individual driver has their own active amp. So XO (active OR passive) takes place BEFORE amplification, lest back EMF will change, on its way to amp output, passing passive XO components.
After that, whatever is damped no longer has much relation to speaker movement, so DF becomes pretty ineffective.
2.
Some amps are famous for having incredible damping capability, based on the genious engineer reinventing Class D amplification.
Bruno Putzeys, first @Philips, then @Hypex and presently @Purifi, gave humanity amps with DFs so high (five digits!), servo systems as mentioned in this thread have effectively become redundant. And these modules start at below 200 bucks.
3.
'Fast bass', although a very subjective concept, is usually indicating a woofer that has dry transient response, among other things (doesn't keep resonating after the punch, sounds completey clear and clean).
Most (even very good) woofers won't give you this, simply because big bass needs big cones that simply weigh too much to stop dead after the signal ceases. Their inertia will force them to keep moving, a little bit at the very least.
The amp will give you this.
An extreme damping factor will immediately remedy this fenomenon. Any out-of-signal movement will simply be cancelled by the amp inverting the back EMF caused by said movement.
4.
If you are using boxed speakers, the 50% of the energy projected inside this box (which will partly pressurize the cone, out of time, so out-of-signal), will coincidentally also be remedied by this high DF.
If you then manage to build a totally inert box, preventing the 50% rear energy loading it's panels at resonance frequencies, this high DF amp is actually solving at least two problems, aside from other qualities it possesses (like virtually load independent frequency response).
And Bob's your uncle.
5.
Do i sound like i'm running a commercial here? Maybe i do, but i guarantee you i have no interest commercially.
It just so happens i love inventors who's brain leaves all other inventors' brains in the dust. Class D exists since forever, and except for being efficient, they were always the worst for hifi. Now they are the only ones able to produce the hights present day hifi has reached.
And i have these amps, they are incredible, they do what they promise, and then some. That just makes me super enthousiastic, so shoot me!