From a measurements perspective, improved driver impulse response could be equated (to some degree, one component) to improved transients.
This translates to small drivers playing respective frequency band, and increased number of drivers to achieve sound power.
Drivers themselves can’t be too compliant (signal reversal, phase shift ) or too stiff (resonances, stored energy, waterfall). Many poor drivers i’ve tested that go into some "high end" speakers don’t cut it, it’s one thing or the other.
A poor crossover design will introduce big electrical phase shifts and so on (nullifying benefits accrued from the above mentioned).
It appears that some big horn speakers mentioned on this thread have defied all physics, engg design, material science, etc and achieved unmatchable transients, as per the sales crew. No, they did not, but, whatever helps to sell your stuff.
What you sell is apparently always the best at everything, no exceptions indeed! (They don’t just win some/lose some as the engineers would admit, but, they just excel at everything according to the sales crew....NOT)