pure conjecture and I’m not a pilot but I did stay at a Holiday Inn.
The tube on the outside of the plane iced over and the computer was receiving inaccurate air speed information.
The plane stalled and the pilots spent as much time fighting the computer as they did trying to recover from a stall.
Assuming they were at approximately 35,000 feet they would have had at least 4 minutes to recover from the stall before impacting the water. They should have been able to recover if the computer let them. Or perhaps they did recover and were too aggressive causing some kind of structural failure.
Other flight crews in similar Airbus ships with the same failures DID recover from the condition. ALL involved loss of altitude, IIRC. this is not the first time it happened.
For whatever reasons, this crew did/could not recover the aircraft, likely from some sort of a stall condition with very limited attitude information available to them.
Again, I fly small, single engine slow-movers with that spinning thing out front. IT is VERY hard to lose control of a Champ, a Tri-Pacer, or a 152, or a 172, or a Rocket, etc etc
I am not sure where you are getting your information... an out of control airplane can use up 35,000 feet of altitude in seconds not minutes. If they lost all of their engines but were still under control they could easily glide for 4 minutes, but that is not the scenario here.