An AoA indicator on the PFD is an option on 737NGs, the 767-400 and the 777. Don't know how common it is though.
Of course using the AoA to fly at the edge of the envelope would be in upset recovery, avoidance maneuvers and the likes -- but in a 'protected' FBW aircraft wouldn't you relie on the protection in such a situation, rather than using the AoA indicator?
Also an AoA will not be garanteed accurate. On jets the AoA sensor is usually not located on the wing, but on the fuselage ahead of the wing; the measure at this loaction will not be the same as true AoA for a number of reasons.
Still, given the importance of AoA, and how many automatic systems relie upon it, of course it is peculiar that the pilot doe not get the same information. Probably has a lot to do whit habit/custom and being trained to measure AoA as a function of airspeed.
I'd take an AoA indicator any day, but I'm not sure how much I'd actually use it.