I'm very curious what the measurements show about this tweeter. When I read of drivers with exotic materials, my audio skepticism tends to kick in, and I'm speaking as a former owner of loudspeakers with exotic tweeters.
Well the material the dome is made from will influence the frequency at which first breakup occurs, but there are other things influencing the overall response of a tweeter too.
The key thing about beryllium is that it has an unusual ratio between density and stiffness.
Most metals have the same specific stiffness, titanium is half the density of steel but is also half as stiff, ally is a third the density of steel but is also a third as stiff, and so on, so all very close in potential performance.
Beryllium and boron both have superior mechanical properties in terms of increasing resonant frequency but boron is difficult to make anything but fibres, they build them up on a wire and it is slow and expensive, so we get boron cantilevers on pickup cartridges but not boron tweeter domes.
Beryllium is also expensive and difficult to manufacture domes in, so will always be expensive.
The shape of the dome also influences its stiffness, hence breakup frequency as well as dispersion.
Given that the stiffness of a panel is proportional to its thickness cubed an ally dome will have a higher breakup frequency than a titanium dome but only by a tiny amount and nowhere near beryllium.
OTOH all the soft domes will break up in the audible frequency range and still can sound fine with the appropriate damping goo applied. It will also "go modal" above its breakup frequency so it starts radiating a bit like a BMR or NXT type device up there, so its dispersion will also be effected.
IMHO having breakup happening in the audible range is something designers know how to ameliorate (it happens in all drivers) but I think aiming for the drivers to all behave like pistons in their working range is a worthy goal, though difficult.
After all most people use static thinking and argument even when discussing dynamic devices (the amount of absolute bollox written about record players is the most absurd) so having a speaker that actually
is working the way most people
think they all do is a worthy objective
Pretty well every bass/mid driver will have breakup in the frequency range where the ear is most sensitive. If the crossover doesn't attenuate this ringing enough it is, IMO, by far the most likely cause of a harsh sound rather than any shortcomings in any tweeter which is "cruising" along un-stressed at these frequencies.