Mitch: I'm hardly any kind of expert (Fiddler aside :-), but since you asked, I'll give it a go.
For dynamic/box speakers, some elements that could be expected to contribute to 'speedy' sound might include making use of high-tech materials science to yield driver diaphragms with very high stiffness-to-weight ratios, and cabinets utilizing construction techniques involving special materials, shaping, damping, and bracing designed to minimize the audible effects of resonances of both the box and the airspace inside it. Some panel-type speakers, particularly electrostatics, are often thought of as having the fastest of speaker sounds, in part because there is no cabinet to resonate, and in part because their diaphragms by nature feature the lightest mass-to-area ratios of any speaker type. However, this doesn't automatically mean that everyone will consider 'stats to sound 'fastest' in real-world use, due to potential factors I won't go into detail about having to do with things like dynamic compression, room loading/radiation patterns, HF extension, amp/speaker impedance matching, and soundwave diffraction, and also because dynamic/box speaker design has come a long way toward evening up the playing field in the perceived 'speed' area.
Other factors that can come into play include crossover design and quality, the manner in which a speaker is physically supported, execution of other driver elements such as surrounds/spiders and the internal venting, cooling, and magnet/basket configuration of the motors, even the quality of the internal hookup wire could play a role (also IMO phase integrity, but I won't go there from here). Basically, it's all in pursuit of achieving a speaker that when an impulse signal arrives, can follow its rise as rapidly and accurately as possible, with as little compression as possible, and then allow for the impulse's die-out to be tracked without being obscured by continued ringing (the storing-up and re-releasing, or the reflecting, of energy over time, both in the physical and electrical realms) of the driver and cabinet.
For your other questions, I do think that in general, higher-powered amps have the *potential* to sound 'faster' in many applications, due IMO primarily to their reduced compression of attacks, and perhaps to a degree because of better driver 'control' (or absorption of 'back-EMF' energy from the speakers). As always though, a better-designed and -executed lower-powered amp will probably sound better in most instances than a less-well-designed and -executed higher-powered amp. In audio, it can be tough to scale things up in terms of dynamic and frequency limits and still maintain sonic quality, or at least get very expensive tyring to do so. In amps, the way in which negative feedback is employed probably has something to do with subjective impressions of 'speed', in that an amp could benefit (up to point - IMO it's possible to overboard with the 'iron-fist' approach, resulting in unatural sound) from having a highish damping factor (lower output impedance) to aid in driver control, but NFB, if used to excess as a design 'band-aid' or poorly implemented, can cause temporal problems in the amp's behavior playing music signals that can compromise its sound both in terms of 'speed' and other ways.
As far as cables go, yes, I believe that some cables do sound 'faster' than others. This is probably a function of both the wire's HF extension in a given application (length, terminating output/input impedances of connected components), and of its propensity to smear signals in time (see description of 'ringing' in speakers above, although in cables the energy storage/reflection is more electrical and less acoustical). To sum up, components displaying little treble roll-off in the audioband, high dynamic limits with low distortion, adequately quick and well-integrated transient response, and low levels of resonance (electrical and/or acoustical) are likely to sound 'faster' than components not as accomplished in these areas. (Anybody - especially those of you more technically qualified than I [which is to say qualified at all!] - wanting to expand on/correct anything I've said here would be greatly welcomed to add their comments.)
