The cost of occasionally having to pay out when AI makes a mistake will be small compared with the saving it gains. It's never going to be perfect. Nor are people though. If a human had made that mistake, then it wouldn't even make the news. AI will keep getting better, but people won't.
I was listening to a guy from Octopus Energy the other day, and he said they get better approval ratings from their AI generated letters than they get from the letters humans write. That's possibly because AI are picking up the "standard" or "easy" replies, and the humans have to do the ones that need looking in to more deeply, but it shows the way we're heading.