> most of the best maths students I know are good at arithmetic/mental math even though we have had replacements for that since the 70s (at least).
Well, consider (for example) the SAT. It used to have math sections both with and without a calculator. Then COVID hit, and e.g. MIT discontinued SAT altogether - now the SAT is back, but all digital and the math section is all-calculator. To me this suggests that computers have integrated into society to the point where one's ability without them is seen as irrelevant. This isn't to say that there aren't holdouts who still advocate traditional pen-and-paper testing, just that they are no longer mainstream. Similarly, I would say for programming, if the questions you are asking to determine if they understand "the foundations of programming" can be easily answered with Copilot or ChatGPT, they are probably bad questions.
As far as teaching, there has always been strong evidence that people can learn math effectively just by playing with their calculators. http://ti-researchlibrary.com/Lists/TI%20Education%20Technol... I certainly learned a few things that way. It is the same way with Copilot - you can actually learn a lot of programming just by playing with it and seeing what "real code" looks like. When you mention fluency, I think you forget how it works - first you write things, then you get used to it and become more fluent. Copilot assists greatly with that first step of learning.
Now it is true, some teachers aren't really good with the Socratic method and other techniques of fostering self-guided learning, but if it is a binary "full access / no access" I would argue full access is better, like how students can apparently use their phones to goof off in class all day without any repercussions (https://news.ycombinator.com/item?id=40495673). There are people who will misuse the access but it is not clear if they would learn anything even without access - it could be that they would just find other ways to ignore the teacher. And meanwhile the rest will benefit significantly - they can look up concepts, ask ChatGPT questions, etc.
And as far as "deep understanding" and the "ability to think and plan abstractly", barely anybody has that, that is not taught in schools. I mean sure there is the watered-down definition of "solve word problems and write essays" or whatever passes for understanding these days, but most of the kids coming out of school are nowhere near the next Einstein, even if they got straight A's. edit: maybe the ability to plan is taught in military training, it's certainly not part of a regular school curriculum.