Does it really? I’ve worked with good programmers who will look thick as two short planks if you ask them to solve a maths problem, summarise a science article, rebut a philosophical argument, analyse a novel’s structure, figure out an unknown word’s meaning, etc etc. We all know STEM people who seem bafflingly stupid outside of their chosen specialties. Those who have well-rounded educations more often seem more smart and able to reason than people whose only tool is the rigid logic of programming/math. I don’t think STEM is an automatic pathway to above average smarts.

That is very much an over-generalization and dramatization. While there certainly are people who fit your description, not all people with math or CS backgrounds fit into that category. Also the existence of such people says nothing about the potential benefits of programming for people with different backgrounds. I didn't day that everybody's only tool should be the rigid logic of programming/math, but merely that learning those skills would probably complement most people's skill set nicely.

That is why I called coding / programming a trade. I openly admit that my interest in most CS topics beyond what is directly applicable to my work is about zero.

Almost everything teaches people how to think. Coding just gets a privileged position in the minds of techies. We don’t see people saying “teach kids to read professional history” or “teach kids dance” in the same way as we see people treating coding like the best way to expand minds.