I don't know where you get the 'cognitive overload' term from (it's not in the article). But it general; cognitive effort is what drives our brains to learn in the first place.
As an organ in an organism, the brain is very adverse to using energy, because the organism might need it later to run or fight some danger. Learning costs energy, and the brain rather doesn't if it doesn't need to. The only reason that the brain will ever learn anything, is if you repeatedly expose it to 'cognitive effort', because in this case the effort of learning will save energy in the long run.
If you use AI so that most things don't require cognitive effort, your brain will not use those learned neural pathways, and they will atrophy over time.
The only thing that the brain learns from using AI is that the most efficient way of doing anything is having the AI do it for you.