Aren't you assuming productivity gains will lead to free time? Why? It never has. Most of us work a fixed amount of time and get paid for that time. Not the amount of tasks we finish if that can even be measured.

Salaries have also not increased with increased productivity long before chatbots came online. So they won't suddenly increase now.

AI is much more just like a new laptop you get from work. The new device is faster, has more RAM and allows you to do more, potentially.

The big question is, if the purchase was worth it. Unlike a new laptop, LLMs are an ongoing cost to users and providers. Nobody except for GPU producers are actually making money right now. Hyperscalers make some of the money back they themselves invested into the companies using their services, but in the end the ROI looks pretty dim for anyone.

So even if there are real productivity gains, you won't see people relax with their kids more. And even if these gains are significant they may not prevent a huge economic collapse so we all will have plenty of time with our kids in the end anyway.