i think a lot of your arguments make sense if you want your child to be a mathematician but i don't see how any of these will be material if they just need to learn calculus/linear algebra and move on to other things (which i think won't be affected by learning math)
though, the better feedback in math is also easily goodhartable. (i personally do not understand number theory or the appeal of number theory, and always have a slight sneaking suspicion that a lot of it is sort of just noticing that simple questions can be super hard to answer
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... and then not getting bored with trying really hard to answer the questions, even though they're not otherwise interesting)
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all this about math being about "seeing into the core of things" cashes out in many ways, but for example, you have lots of physics insights coming along seemingly necessarily with tough math, eg electromagnetism (field theory), GR (riemannian geometry), QM (hilbert spaces)
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