A bit off-topic, but I'd like to reference my own trade (when I had one): high availability IT. This is usually accomplished by having all critical components duplicated, with one active and the other standby*; and the two in permanent communication to determine the status. If the one says "temperature is 15 degrees" and the other says" temperature is 25 degrees" then there is a problem, called a "split brain" situation, which is normally solved by adding a third component, called the quorum device. Funny how totally different technologies apply the same tactics.
And indeed the cost and complexity of adding a third AoA sensor to a plane as complex and expensive as an airliner must be more than bearable - Boeing certainly spent a lot more money now.
* this is called an active/passive setup; there are other configurations, load sharing and what not, but let us not diverge too far