There is an option (according to Chris Brady) of AoA indication for the 737 which even has a nice green band for approach AoA values. I do not know if there is any airline out there using it or if it is rather used by military applications.
We do not have that on our 737s, however we had several AoA vane failures about 1.5 to 2 years ago and all of them were pretty confusing to the crews as pretty much every other interesting value (IAS, altitude, even ground speed and wind information) will be way off its real value, often in quite unpredictable fashion. One most probably played part in a runway overrun, all others were in flight.