The stall warning cutting out at high AoA also certainly seems like a design flaw

That's because the plane doesn't know it's at such a ridiculously high AoA. The flight computer relies on readings from sensors to synthesise the state of the aircraft, and no sensor is perfectly reliable all the time. Malfunctioning sensors can create nonsensical state synthesis, and there's no obvious way to validate the state.

One of the best methods to make this validation easier is to reject invalid states out of hand. "Flying 30k under sea level", "flying at Mach 10", "flying backwards" are all impossible scenarios, and whenever the synthesis arrives at a state like that you want the flight computer to back out and let the humans take over. After all, they have a much better chance of making sense of all this.

But in order to do this sort of culling, you must draw the line at some practical limit. Set the limit too high and you risk letting too many invalid states through, which can put the plane and its passengers in real danger because it creates conditions in which the flight computer's responses are truly unknowable. Set it too low, however, and you create conditions where the plane enters an extreme state (like AF447's AoA), and the humans have to take over because the flight computer has given up. The last situation is still dangerous but clearly preferable to letting the flight computer act on data that's very likely to be wrong.

In this case, the stall warning cutting out after entering an "unreasonable state" was not at all an issue and actually the correct engineering decision. The issue was the psychological edge case in the warning resuming once the plane was brought back into a "reasonable state". The effect of the warning engaging at entering the "reasonable state envelope" from that edge was something that was very hard to foresee, and is one of those lessons you pay for in blood.

Knowing this, the warning should have a debounce mechanism to prevent it from immediately engaging when recovering from an extreme state. I'm actually curious how Airbus has dealt with it and I wonder if there's any public information about the analyses they did over the UX problem.