The elephant in the room here is surely that:
a) Any computer taking the place of a human pilot will have to be able to think, predict and plan as well as a human. This means that humans will need to be able to model the human brain in a computer.
b) Any such computer will be built and programmed by humans.
c) The 'computerphiles' are assuming that such a computer will be 100% reliable and never have a bad internal connection or a memory fault or a CPU conflict.
So they are talking about a system on aircraft which will also be made by humans and that will introduce another whole set of potential glitches and software errors. Not only that, but there will be no pilots on the aircraft to sort the problems out when they arise. Would you put your family on such an aircraft?
Computers are excellent at assisting humans. They can hold a course and a level while the pilots oversee the navigation. They can provide numerical data such as landing distance required. They can augment pilots' control inputs to avoid overstressing the aircraft or cause accelerations of more than 1g etc. etc. But they cannot conduct a flight.
Those arguing for computers to replace pilots are obviously not current commercial airline pilots themselves, and therefore do not appreciate the full potential complexity of conducting a flight.
They also, I suspect, have never actually programmed computers themselves, (as I have). If they had, they would realise how difficult it really is to make a computer register and react to any and all circumstances as a human can.
Yes, human pilots over the years have cocked up and crashed, and that is a terrible thing that nobody wants to see happen again. BUT Instead of arguing for computers to replace us, let's argue for better training and conditions for pilots. This is an area that has been declining in recent years owing to the competition of low cost airlines etc., and is the real area where changes need to be made.