Does a pilot really need a stall warning at <60kts/AoA > 35deg to tell him or her that the aircraft is stalled?!
FWIW:
If the airspeed indicator isn't working, and pilot is on instruments, a possible answer to that is "yes?" (Or, if the AS indicator is working, but the pilot thinks it isn't, and is on instruments ...)
You ask a good question: does that make sense as a design case?
But even if one accepts that as a possible reason to display AoA ... one is still left with an instrument scan, and all of the other cues, none of which are seat of the pants.
What is Attitude Indicator telling you? (Pitch & Roll, turn & slip)
What is Altimeter telling you?
What is VSI telling you?
What is the Thrust/Engine indication?
What is are your configuration display telling you (flaps, gear, etc)
I am still wondering, and will probably not get the answer to:
What did the PF see? Where was his scan taking him?
Hopefully, info from the CVR will eventually reveal what PNF's response was to the climb from FL 350 toward FL 380?
What did he see, what did he say?
EDIT: to make sure I understand correctly
Stall Warning is intended to sound/go off at an AoA less than stall AoA.
Point being (like stick shakers or rudder shakers on various aircraft) to cue pilot to act to prevent the stall. Stall warning would remain on until AoA goes below that value, to indicate either "you are still close to stall" or "you are stalled" either of which is a cue to do something to unstall the aircraft, or get away from the stall threshold. A simplistic way of translating Stall Warning is "change your AoA, it's too high" as noted in various posts in this and other threads.
(Yes, pitch and power remain the basics).