Good post.
A couple of nitpicks...
Similarly, a lot of modern medicine is rational, but not too scientific. A doctor sees something and it looks like a common ailment with similar symptoms they've seen often before, so they just assume that's what it is. They may run a test to verify their guess.
Actually, this illustrates scientific thinking; the doctor forms a hypothesis based on observation and then experimentally tests that hypothesis.
Even math curriculums are structured around calculus instead of the much more useful statistics and data science placing ridiculous hurdles for the typical non-major that most won't surmount.
Actually, the natural sciences (physics in particular) are heavily dependent on calculus. Ditto for engineering. In fact, a solid understanding of Bayesian statistics requires a grounding in calculus. So, I don't think it is true that statistics and data science are "much more useful" than calculus.
I was struggling to word the doctor parapgraph in a manner which was succinct but still got the idea across. I think query worded it better.
On math curriculum, that advanced classes build off of calculus is a function of current design. They could recenter courses around statistics and have calculus be an extension of it. Some of the calculus course would need to be reincorporated into the stats courses, but a lot of it wouldn't. You're going to have a hard time convincing me that trigonometry a̶n̶d̶ ̶v̶e̶c̶t̶o̶r̶s̶ are a necessary precursor for regres...