AoA is relative to the airflow, you cannot measure that with gyros.
Actually, yes, you can, and the 767 tanker does compare the AoA vane with the gyros. Most unmanned ac do not have AoA vanes, and rely on the inertial system.
Interesting paper showing the results of using different algorithms to estimate AoA
http://www.tc.faa.gov/its/worldpac/techrpt/tc16-52.pdf
Always amused by the CAT designations...from the draft FSB
Aircraft Category
B-737 C
B-737-CL C
B-737-600/700 C (even a 700 at CAT C is a struggle)
B-737-800/900/900ER C or D (CAT C?)
B-737-MAX C or D (CAT C?)