Lyman;
I am not sure how ACARS would report the FPV not working. I suppose it is possible. The Bird is not a "thing", it is calculated from the IRUs, and represents the course, both vertically and
horizontally, that the aircraft is moving. It is completely unrelated to any pitot static system, and does not rely on AOA measurements either. There are 3 IRU's on a 320 (maybe one more on a 330?). Any one of them could calculate the FPV.
The ACARS could report that the IRU's were not working, which would mean the FPV is not working, but I don't remember that from the data that I have read. It was only pitot-static information that was bad, for a short time, during the accident. At least that is what I have read thus far.
I flew 3 different jet aircraft with AOA as the primary performance instrument. The last one also had a HUD with the FPV. The great thing about the FPV on a PFD is that it gives you instantaneous information, including AOA, irrespective of what is going on with the pitot static instruments, and does not require any additional "scan" . It is where you are looking most of the time anyway.