Advantages of beryllium?

In terms of the diaphragm, both Al and Ti have very similar stiffness with a given density. So when shaped, the weight will be quite similar between the to when targeting a specific stiffness performance, but the titanium part will thin in comparison due to its much greater density. Titanium will be somewhat more forgiving if over driven or out of bandwidth as it has greater internal dampening as compared aluminum alloys. So while Ti is a touch better than Al in overall performance, there is an added cost to its source and manufacture.

Be on the other hand can perform at much higher levels than either Al or Ti. A higher modulus than Ti and lower density than Al. This causes it to be highly damping, but not internally. Being very rigid, a Be diaphragm maintains is shape under a significantly high stress, but internal dampening is more about specific elasticity and this is where Be and Al share a commonality as neither have much elastic capability. Ti actually has quite a bit more elasticity, especially for a metal. So with Be or Al, its important to not go beyond the designed capability. Its important to do so with any driver, but the resulting output distortion will be higher. The designed capability will be very driver specific as the shape, size, thickness, quality of process will dramatically affect these figures. FEA applications will be primary point in the design process for modern drivers.

When Be is being formed, the dust that can be inhaled that can be hazardous. When formed in shape, its pretty stable and even when broken isn't quite as hazardous as it would be in a manufacture facility with volumes and processes being applied. It still needs to be handled appropriately in those situations.  

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.