I wouldn’t equate trigonometry, which underpins the classic parabolic example you’re referring to, with critical reasoning in human conversation. One is situationally useful at best; the other is mandatory to prevent exploitation by malicious people. Mental quadratics may be appealing, but the ability to reason is the bare minimum. Besides: if you’re using a calculator or AI in a board meeting, you’re likely unprepared for the board meeting.
I'm not sure how you did proofs in trigonometry with a calculator.
I ran my school district out of math to teach me in the 80s and ended up focusing on sysadmin in the 90s rather than repeating trigonometry or pursuing formal math at the local college. Sorry I can’t be of more use to your argument! Perhaps someone else will have applicable experiences.