This is a pretty tough problem, different than self-driving cars because people see driving as something easy, but flying is seen as hard (just look at the difference in training and salary between a bus driver and a commercial pilot). Trained pilots/meat-computers will soon be worse than an automated system 99.99% of the time, but in those strange 0.01% corner cases the meat-computer really shines. There are several cases like Flight 214 (https://en.wikipedia.org/wiki/Asiana_Airlines_Flight_214) that computers would have helped, but there's still a few "Miracle on the Hudson" that any computer short of a general AI would have botched (https://en.wikipedia.org/wiki/US_Airways_Flight_1549). It will take a lot of work to get to where people will accept an automated flight without a safety pilot on board, and if you have to pay a safety pilot to ride along, you aren't saving as much money.
> even if the airline passed the cost savings onto me
HA! Like that will happen. The only time that airlines "pass on cost savings" to the customer is when a low cost carrier starts offering service for the same route.
Comes out to ~$7 cost savings for two pilots per flight. Doesn't seem that impressive for a long-haul unless I'm missing something.