i think speed in a speaker mostly refers to the mid and upper bass 50hz-250hz region which are the power frequencies where the music lives. vocals, drum kits, pianos, cellos, horns.....they all fall down or rise in this area.
leading edge precision and the presence or lack there of ease and refinement in these frequencies either impart flow and energy to the music and maintain the timing or muddle and restrict that flow and energy.
this is a speaker-amplifier-room issue, not just the speaker. and typically you see a crossover right here, amps struggle controlling the drivers here, and rooms have most of their worst bass nodes in this area. as you increase the dynamics and SPL’s this will be where things go to hell first as the combination of the speaker’s limitations, the amp and the room acoustics all rear their ugly heads.
but get the crossover out of this region, have sufficient driver surface to limit the need for much excursion, and appropriate amplifier for the speaker draw, solve the room issues, and you can get the ease and effortlessness and the speed and precision of the music will result in that speed that serves the music, the music breathes and soars.