Which is the complete opposite of what I would do. Id be actively teaching this new learning tool to the maximum.

That perhaps classrooms being >30 students and overworked teachers doesnt need to be solved, instead the endless questions from students could be sent to regulated AI options. Making the teacher's job that much easier. Perhaps even on average ending up with significantly better educated students.

>Should governments, teachers, heads of ministries up the priority of compensating the negative offsets in cognitive abilities due to the use of AI or will the progressive improvement of youngsters in/with/due AI use be enough?

There's a great deal of sensationalism, fake news around this at most.

I have more information about Calculus for the first year of the university here in Argentina. Officially nothing changed, but we are not teaching some of the weird substitutions for integrations, like x=sen(theta) (or it was in the other direction?) for Integral[(sin^3(t)+cos(t))/(sin^5(t)+7cos^3(t))dt]. Wolfram Alpha can solve it, and unless you work in a very specific are it's not worth.

Linear substitutions like x=7t+2 are very important, and students MUST learn that. Not linear like x=t^2+1 are very useful and there are a lot of interesting tricks, probably worth learning.

Integration by parts, I'm not sure. In the first year it's only a nice trick but it's useful for some statistic results, like Integral[xe^{-x^2}dx] that have a lot of applications that are studied by many careers without more math courses. It's also useful in some branches of advanced math and physics, but perhaps it can be delayed in those cases.

A big chunk of teaching if giving a general understanding of the topic, later they can use the integrations tables, Wolfram Alpha or AI. It's very hard to understand the topic if someone only types the question in Google and copy whatever Gemini says. Some may claim it's important to teach critical thinking, but that's even harder than integration and it's even harder if someone wants to think critically about the AI results with zero understanding of the simple cases.

Back to your question... I don't know how the government can compensate that, unless they add 2 more years to high school. But everyone will complain and they will lose the elections and everyone will continue complaining.