Given the choice of a bored call center employee who doesn't care, or who's only pretending to care, and who isn't really empowered to fix a problem versus an AI bot that can actually effect real change to fix a simple problem, of course people prefer bots.

That's a false dilemma though. People would actually prefer a person who can fix the problem.

However ... what people really want is a service where things work well enough that they don't need to contact customer services at all. Somehow I doubt British Gas are going to make that happen though.

This is why customers ask to talk to a supervisor - to get a human who can actually do something. But if the choice is between an AI and a human who is only allowed to follow a script, is there really much difference?