Even if properly designed, a metal cone/dome will behave like a piston only up to its first structural resonance frequency. There isn't much inherent material damping in metals, so any resonances are going to have a very high Q. This is clearly apparent in the audio passband when bass-midrange drivers make use of metal cones (and usually a bit above 20 kHz for tweeters). Even though the crossover may heavily attenuate those resonances, is it wise to have them present in the first place as a result of a poor choice of material, when better approaches are available?
What is meant by the characteristic sound of the cone material when it is breaking up? Doesn't a cone material simply possess properties of density, stiffness and loss factor (damping)? Aren't those the fundamental material characteristics that are needed to be identified when engineering a new cone design? How do any of these engineering properties translate to a "characteristic sound" if the frequency response of the driver is ostensibly flat? Isn't the audio performance simply a result of the structural resonances, damping and piston-range behaviour of the cone, and not the "material" per se?
The following might provide some guidance. In terms of audibility of different materials, back in 2010, Rotter and Lindau published a paper titled "Audibility of tweeter performance beyond spectrum and phase" (
PDF). They concluded that (emphasis added):
"
When eliminating frequency and phase response irregularities, baffle and room interaction, non-linear behavior, and distance effects, a blind-comparison listening test could not reveal audible differences between different types of tweeters. Neither the material nor the actuator principle, neither the tweeters geometry nor the specific form of wave fronts in the far field could be shown to be distinctive features of different tweeter types. Divergent results of previous studies can only be explained by aforementioned shortcomings of the test designs. Furthermore, when excluding room and baffle interaction, FIR equalization seems to be capable to compensate for the behavior of different loudspeakers at the sweet spot within a typical range of horizontal head movements."