Pitot tubes icing over is common on all planes not just Airbus planes. It's more or less expected and planned for.
There’s three pitot tubes. There were ADs issued over them icing over. Airbus replaced them multiple times with tubes from different vendors.
In the final report, the first major issue is “Temporary inconsistency between the measured speeds, likely as a result of the obstruction of the pitot tubes by ice crystals, caused autopilot disconnection and reconfiguration to alternate law.”
Icing over of pitot tubes seems more significant to me than I think you’re making it out to be.
How did they not notice their altitude was climbing as they pulled the plane up - they got into a CLIMB rate of 7,000 feet per minute - that's STUPID! WHY climb like that? This has nothing to do with airspeed.
The stall alarm goes off 75 times!
They reduce power to idle for a bit??
It's total nonsense, anyone who has flown a single engine cessna for 200 hours or more would have been able to get out of this easily just based on stall buffet and stall alarms.
There are aircraft, for example the B-2, that can't fly at all without working pitot tubes.