Stall warning
The maximum angle of attack (i.e. where the plane stalls) must depend on a number of factors - pressure altitude, airspeed, load factor, aircraft weight, config. Lots of points of failure for a measurement system.
I'm not sure if actually displaying a raw AoA it to the pilot would be so useful - otherwise every C152 would have such an instrument. How would the pilot know what is the current alpha-max?
The Airbus FCOM states that in case of a simultaneous OVERSPEED and STALL WARNING the stall is to be actioned - failsafe: if a pitot fault gives us an excessive speed the alpha-max will decrease, so if we follow the stall warning we basically end up flying a lower AoA then would otherwise be possible. But the 'under-speed' scenario does not seem to be addressed too well.
Now the types I am more familiar with - the C152 and DA20 - have a stall warning system which is basically an orifice on the wing connected by means of a tube to a little buzzer - it detects when the air pressure on the wing suggests an oncoming stall. This system is far superior to what the A330 has in one respect - it is completely independent of the airspeed system.
Now - why can't the Airbus/Boeing engineers devise such a system for the big jets? I do not suggests orifices, tubes and buzzers - rather - pressure transducers (or perhaps strain gauges?), a data transmission network and a clever computer to work out what is actually happening with the wing. A system which tells us if the wing is generating lift or not, how much lift, which part of the wing is stalled.