Productivity is typically a broader scale measure against the economy. I 100% agree that the shoehorned adoption of AI into general company processes is more of a negative than a positive. Most people here would agree that AI has only really affected productivity positively in the past 6 months-1 year. So obviously there wont be much general uplift across all industries yet, and obviously that would mean there's not really enough data to go off of empirically yet.
Beyond data and vibes though, I can't think of a single technology in human history that had a forced adoption quite like AI does. To the point where it should be pretty obvious to all of us that a large group of people are going to push back and be unhappy that it's disrupting their work. That doesn't mean that the people who actually like the technology wont find more productivity with it though. It's just when measured against a sea of forced adopters you'll never find a general uplifting trend. People typically don't like change.
With the most politeness I can muster, show me the data. “In God we trust. All others must bring data.” If the data doesn't exist supporting the productivity improvement assertion, ¯\_(ツ)_/¯