In the same way as the Go master (perhaps) feels disillusioned by being beaten by the AI, I think people in general will not accept humans being replaced with machines in some "special fields". In those fields, the customer/user, will not experience the same utility if a robot is doing the service compared to another human, even if they are indistinguishable.

I think an interesting issue here is that in the (far) future, many services could be performed cheaper by AI/robots and in such a way that the customer is unable to tell wether a human is involved or not. And in this future, humans will probably be a premium service.

Take motor sports for example. We can probably now/soon replace F1 drivers with algorithms and cameras, but nobody would pay 1000's of USD to watch them drive around in Monaco. If it would turn out someday that the drivers had been replaced (for safety reasons or whatever) without telling the fans, the outcry would be tremendous. And even if outcry does not always equal "true utility", I think it highlights my point: humans made of flesh and blood risking their lives or performing extraordinary feats have an intrinsic economic value that can't be replaced.