Allow me to comment to the issues, adressed by OC at Diagnostic.
OC
Supposing the crew were surprised then training should kick in. A pause, a scan of the instrument panel (and remember the only instrument that was not reliable was the Airspeed Indicator).
The crew was surprised, not by the UAS event (which was not identified yet), but by the drop out of the AP and the need to fly manual. That sudden manual flying chewed up most of the crews attention and was hindering in identifying the cause of the problem (UAS). This cause could have been multifold including the WX situation/ turbulence. The minimal hand flying skills led to the zoom up.
OC
PJ2 also pointed this out - this was not a serious incident at first. However, the crew actions made it into a serious incident. It also seems that the PFs scan broke down almost immediately and that the PNF did not intervene sufficiently. So a UAS warning might not have made any difference.
It could have made a difference from the beginning. Knowing, that the problem of AP drop out is UAS, or even knowing it before the AP drops out and manual flying is imminent, saves time in analyzing the situation and helps initiating the necessary steps. The zoom climb would have not been part of the procedure, as often mentioned before.
OC
The cockpit voice transcript indicates a very rapid 'over reaction' to the initial incident. Once again this is not indicative of an interface issue. There was no attempt to use the SOPs or to diagnose the problem.
Because the initial incident was not fully identified. The sytem knew that the speed became unreliable, but the indication to the crew was the the handover to manual flying in some expected turbulent WX situation without communicating the known information (UAS) of the reason for the handover.
I go with diagnostic, most of the other mentioned UAS events had not been handeled as they should have been, and in most of those cases the identification of the UAS was marginal, late, or not existent. There is lots of room for improvement, not only on the training issue.
IMHO MIL crews are trained to work around the unexpected event / problem, as they canīt plan a military mission and the asociated tasks in great detail, and if they can do it, it anyway comes different to the planning in the end due to a multitude of possible factors including bad guys trying to shoot holes in your plane.
But air transport crews are best trained in handling standard and non standard situations acording to SOPīs and CRM. To implement those procedures the identification of the problem has to be quick and simple and is a prerequisit to implement the correct procedure. The ECAM is the best example for that need.
Even when PNF mentioned "..we have lost speeds..." , we cant be sure, that it dawned onto them that the AP-disconnect had anything to do with the missing speed indication and was initally just a simple UAS situation. Because it was neither acknowledged by the PF nor was the necessary procedure mentioned.
The first necessary step " maintain aircraft control" was already hindered by the unknown cause of the problem and the lacking manual handling skills. Would the cause UAS have been known from the beginning, his handling might have been simplified as PJ2 sstates by doing nothing. But instead they failed in " maintaining aircraft control" , did never "analyze the situation" and could therefore not "take proper action".
It comes down to a misidentification of a problem (UAS), which could have been communicated to the crew by a clearer and more expedite way.