Bayesian methods say that when presented with statistically rare events, such as a failure behavior of the system under test, we are better off throwing the system away and starting again.
Correct,
when viewed from the perspective of the software designer. But while the pilot has the luxury of throwing systems away (flying the plane manually) the pilot doesn't have the luxury of rebuilding complex software systems on the fly. He has to deal with the failure as it is, in a few seconds, with many lives at stake.
You can't expect humans to debug real-time programs magically as they go wrong, if they go wrong. So they had better be right. And that is where the math comes in.
Exactly. And I'm in full agreement with you so long as we understand "right" to be statistically right, that is probabilistic.