I put my family on a driverless train (in docklands), and there's not really that much difference between train drivers and pilots so I suppose in principle I would.
Scenario 1
DLR has major computer failure
DLR stops moving, or at worst DLR hits something and stops. Ambulance crews have quick access to injured.
DLR computer issue resolved
DLR starts moving again if undamaged.
Scenario 2
Aircraft computer goes wrong
My family and I hit the ground like a brick from six miles up.
Not quite the same. I can step out of a stationary train, this is a major step change.
Let's be honest, it's not a question of trust, I work with tech every single day and we manage failure every single day. Actually we manage unforeseen failure often too and even safety criticial software goes wrong, the current concept of human beings supported by safety enhancing software is a good one. Why remove the human back up element? Easy, cost.
I won't fly on a pilot-less aeroplane any more than I will fly on a windowless one commercially. Automatic cars might well be a thing but only for major towns and cities. Motoring is about real freedom to far to many people.
Remember they said vinyl would go, DVDs would disappear and video would kill the radio star......