Should you do any of those follow ups? Seems like a judgement call. In my experience strengthening those fundamentals is important, but there are many occaisons where the point of the exercise (such as learning to write legible long form algebra) overshadows other possible benefits - making a crutch such as a pencil and paper, or a computer typing system, the appropriate call to make.
Please, when you pose 'absurd' hypotheticals, follow them to likely or reasonable conclusions. If you shit your brain off when the conclusion seems obvious but before evaluating you will frequently end up just asking reasonable (if somewhat obvious) questions.
But after your comment, a lot of what I see around me are crutches. The keyboard I type on, the heated building I'm in. They really help me perform "normal" functions, and living without them would be a handicap, so they are crutches.
But I see no point in purposely living without them. Live your life, and don't force yourself to do something you don't like unnecessarily.
Where the line is for necessary/unnecessary dependence lies is a judgement call.
The point isnt to accept a heuristic that points one way or another, but to be conscious about it being a choice that we can make that can have various trade offs along a spectrum. As usual figuring out what trade offs to make is highly dependent on what your goals are.
Why bother with the effort of learning anything if you can just be lazy and look it up in a book!
Yes. When was the last time you used that algorithm versus breaking down the problem in your head?
Whereas a pencil has no assumptions whatsoever, and no bias towards what you'll do with it, and offers no suggestions that might funnel you in some direction. That is what good tools are like.
Of course, we can't take ChatGPT for granted like a pencil, because it's controlled by a third party and requires resources out of reach (for now). But it might become trivially cheap one day.