"Faster? I would ask you to define what you mean by 'faster'.

Transient response: a result/function of frequency response."

Transient response is a result/function of frequency response. For each driver this is essentially correct. There is a direct correlation between transient response and steady state frequency response.

Faster?

All drivers including electrostatic and magnetodyamic have a group delay which is the time interval between the application of voltage and the mechanical response of the armature and attached vibrating membrane whether cone or film. The so called "time aligned" speaker usually results from an attempt to match the group delays from one driver to the next in their crossover region.

Overshoot occurs when the inertia of the cone overcomes the control of the magnetic force of the armature/stator and the cone does not follow the applied electrical waveform exactly. This will show up as a frequency response irregularity (resonant peak) or even in the extreme as a non linear distortion component. This is usually almost nill in most high quality drivers except perhaps underdamped woofer cones in poorly made speakers or improperly designed enclosures. The motional response of the entire drive assembly regardless of the principle follows Newton's second law of motion as applied to forced resonance. Amazingly, both the Theil Small parameters and the design of acoustic suspension enclosures have accurately modeled their equations on Newton's law. (to the degree that they agree with Newton's second law, they are right. To the degree that they disagree with his second law they are wrong.)

What is radically different between planar type speakers and "box" speakers and IMO accounts for the major difference in sound is the spatial radiating patterns. Box speakers have their sound eminate from what are essentially point sources and usually directed in just one direction. Planar speakers eminate their sound more diffusely from a much larger surface and are often bipolar. This is absolutely necessary to produce acceptable sound pressure levels because the maximum excursion of the planar membrane is very limited compared to dynamic loudspeakers. The ability of planar speakers to emulate sound pressure levels of large ensembles like symphony orchestras, instruments with deep powerful bass like pipe organs, or popular music amplified to loud levels is usually inadequate by a considerable margin. Planar speaker designers haven't yet managed to overcome the limitation of the ability to move large quantities of air. For many people, this alone makes them fatally flawed. Installation if they rely on bipolar radiation is also a serious problem for many would be users because they have to be placed several feet in front of a wall reducing the effective room size. The high frequency radiating pattern of many planar speakers is also surprisingly highly focused at least horizontally. This is overcome to a degree if the radiation is bi-polar taking advantage of room reflections of the rear radiated wave. This effect can be duplicated in dynamic loudspeakers by using a multidirectional array of tweeters where at least some of them are rear firing. Many of the best speakers use this strategy and I have modified every speaker system I own and listen to seriously to incorporate it.