Advantages of beryllium?

Highly rigid and light but poor internal damping.

Personally I don’t like the splashy sound of drivers of this type design (metal and highly rigid). They have great bandwidth that makes for impressive measured performance but I find the sound is "splashy" due to the way rigid materials vibrate naturally (like a bell vibrates and rings after an initial hit but a damped material like a pillow does not).

Splashy is a good term - as in when you splash the water it makes a lot of sound after the initial splash. Acoustically this means the driver imparts its own sound to the timbre whereas an internally damped cone material is much more inert - contributing much less coloration after the sound stops.

I prefer damped designs even though they tend to have a narrower bandwidth and can suffer from breakup and therefore require more careful design and larger more expensive drive motors. Damped cones sound much more natural and faithful to the original tone/timbre of recorded instruments even if they are not as linear on a speaker frequency plot.

Here is an example of a titanium tweeter - look at the ringing in the waterfall plot in the treble !!!

https://www.stereophile.com/content/jmlab-utopia-loudspeaker-measurements-part-2

Here is an example of Be - similar problem in the treble but very much better than titanium

https://www.stereophile.com/content/focal-maestro-utopia-iii-loudspeaker-measurements

beryllium is 1/3 lighter than aluminum yet 6x the specific stiffness of steel

IIRC, it outclasses Ti in that way - dunno re stress cracking but the newest Ti alloys are better than their reputation

the dust is highly toxic - ask Porsche who used them - briefly - on brake components of some race cars

might be fun to see if the German govt. allows Be in speakers - you can get away with putting toxic liquids in cables in Canada and importing them into the US though

If a Be tweeter is properly constructed, there won't be any ringing in the audible band and well above it. While it has very low internal damping, implemented properly it is considered what would be called high damping, so rigid that it really doesn't resonate.

Now as for those delayed energy charts, look through all the measurements and read the comments. In the older Utopia, the mid driver wasn't well isolated and was impacting the tweeter and it does reach its breakup point is at 22khz and certainly does show. So there is a number of issues that design resulting in that measurement. Focal also didn't develop a great driver in this case as we have seen many other metal drivers of lesser material measure extremely well in the decay plots. Even Al, which should be one of the worst materials but has resulted in some of the better measurements is mainly due to the quality of implementation. The material certainly has an impact, but its use in design matters more. 

https://www.stereophile.com/content/kef-r700-loudspeaker-measurements

The Kef R700 uses a plebeian Al dome, but due to a designed shape and stiffening ring, measures perfectly clean. Kef uses just an alloyed version in the Reference and Blade series and gets the breakup point beyond 30khz. Associating a sound with material is for the most part is invalid and proper design and engineering is the correct answer. You can just as easily implement a fabric dome poorly and have messy decay plot due to energy coming elsewhere.

Those Focal speakers didn't achieve their designed goals and they likely knew it. Reached the end of the cycle and budget and released the product as it was, being the best they knew how to produce at the given time and a given cost. Looking at the Sopra 3, they still haven't quite gone as far as some other companies in spectral decay, but progress has been certainly made.