Or, maybe, the AI companies making claims about increased productivity due to their models are wrong (in most cases)?
They are not wrong, they're lying. Very important difference. There are a lot of people who will say "I'm getting mega productivity boosts" who aren't getting financial returns from you believing them; those people are wrong.
I've never heard any such claims but meanwhile in my actual job I'm seeing unbelievable productivity gains (in terms of actual cash spent before and after vs the same kind of work being done).
I dunno: this is pure anecdata but software engineers I know well - including me - all say they’re delivering multiple times faster, so it’s definitely good for something.
I don’t know about other tasks, but it’s pretty rad for coding, testing, DevOps, and config.