Cone speakers have to overcome inertia (says obvious man) so need to be tightly controlled in their back and forth movement. That said, it seems to me that the lightest, stiffest
cone materials should be used
As mentioned, the inertia problem can be compensated by proper motor, force and control (with the exception of true resonators like port vents), I would consider it as debunked when it comes to explanation why some speakers are described as ´fast´. Many speakers which are described as ´fast, precise´, employ pretty heavy diaphragms, particularly in the bass region (closed-box designs, dipoles, fullrange horns).
If you say the stiffest cone material should be used, this is an obvious contradiction to claims that planar transducers are superior. They - particularly electrostatic planers - are anything but stiff, and both force and control relative to the diaphragm area are inherently poor (hence the resonance issues with many models).
Having heard a legion of statements which different types of loudspeakers are described as ´fast, precise in timing´, I could offer a different explanation. I would suspect the reason for this mainly in the bass region and lower midrange, particularly the audible decay of resonances and reverb. In contrary, some loudspeakers causing audible booming, long resonances and midrange-heavy reverb in the room, are regularly described as ´slow, incoherent in timing´. Many of them can pretty much reverse this character the moment you listen to them under free-field conditions.
If my hypothesis is correct, it would mean that not the transient behavior is responsible, but the interaction with the room and the resulting decay. That might explain why dipoles, fullrange horns, cardioids, line sources, planar electrostatic, planar magnetostats and many more are equally described as ´fast´, as their radiation pattern helps preventing room problems in the lower frequency bands.
