Firstly, GDP is a bad measure of productivity. A pill that replaced all healthcare would reduce GDP by 15%, but I doubt anyone (even economists) would call that a catastrophe.
Productivity has stalled mostly because people have already filled their needs, so it makes little sense to buy more. Basically everyone have the clothes they need, the food they need, the car they need, the computer they need, already. Screen entertainment and information is basically free nowadays. So no matter how much you increase productivity these sectors will remain mostly constant.
What do people still buy? Housing, but that is mostly a competitive good, people spend as much as they have on housing and it is limited supply so prices just increases to whatever people can afford. Same thing with education, international flights and the free market healthcare with restricted supply you have in USA.
Another thing is access to other peoples time. You can buy a person to clean your home or do your lawn or drive you somewhere or renovate your kitchen or provide a massage or other things. There is no way to significantly increase that productivity, it is mostly fixed.
So personally I see no need to increase GDP (what he calls productivity) further. Not to mention that many things gets cheaper, a family buying a TV today gets a much better TV for the same amount of money as a family buying a TV 30 years ago. The main thing would be to automate tasks so you no longer need as much access to other peoples time, but that is mostly an unsolved issue for now. Automating information delivery worked great, but it didn't lead to increased GDP rather it lead to those products becoming essentially free to consume effectively making it useless from an economists perspective.