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Not sure why you got down votes for this because you speak the truth. It reminds me of a time when I was in a lower division Physics class and the professor announced to the class that calculators would not be allowed during the test. Since most of the class was made up of engineering students there was much wailing and gnashing of teeth. But the professor explained that calculators wouldn't be needed because if there was any numbers at all in the answers they'd be trivial to calculate. This came as quite a shock to a lot of students who'd been equating math with numerical operations.
Probably downvoted for making hyperbolic generalizations?
Also, your anecdote about kids feeling more comfortable on calculators has nothing to do with what is or isn’t math, and comes off as another kids-these-days story.
I hope I never find myself in that spot with software. This talk has the right mindset that it's possible to figure out just about anything if you dig deep enough, but a) you have to put in the work to dig, and b) there's seemingly infinite depth so we have to keep a humble and open mind.