At a bare minimum, the basics of algebra (and to a lesser extent precalc, such as understanding limits and differentials) foster a type of abstract thinking and skills that pretty much anyone can benefit from.
Everything else you've listed can be acquired as a dishwasher or a line cook.
Anyways, the classes always seemed to me to tend more towards shut up and calculate than they did building a robust understanding and perhaps most important of it all: a mathematical intuition. I always found it profoundly stupid that there were never any essay questions in math, I expect those who elect to teach the subject are often wont to expediency (which would explain the number of coaches in the department) rather than an inclination towards the subject itself.
Students who didn't show an interest in higher maths courses either took slower versions of the earlier courses where they could get more time with the material, or more business oriented maths such as basic statistics and accounting.
AP Calculus was the closest I experienced to "shut up and calculate", if only because our teacher somehow managed to get behind the lesson plan in our first week and we ended up doing homework for lessons the night before the class where she would actually explain it. That was the second most brutal experience of my academic career, only after the semester in college where I was taking a macro economics course taught by a Polish grad student and a micro econ course taught by a Greek grad student; neither of them pronounced things (especially, and perhaps obviously, the greek letters in equations) the same way, and it turned into a nightmare keeping things straight.
I wonder if you could get a professor to do anything more than plug and chug, and that's a skill we've long ago delegated to glass. Not only do I want to explain these things in my mother tongue, I expect to know why some variable is in some such place, and how a cube of some other variable is related to the problem at hand. Calculation is banal.
To illustrate my point of the uselessness of our conventional mathematical training. ChatGPT gets a 700 out of 800 on the SAT Math section, but ask ChatGPT a reasoning question that requires math... it can't do it. That shows you just how useless the SAT actually is except for training kids to pattern match.
On the other hand, GPT 3.5 is painfully bad at basic arithmetic. Apparently it can add long numbers, but you actually need to explain the addition algorithm and give it some examples. Then it can walk through the process step by step, just like an elementary school student.
In a lot of cases, I suspect ChatGPT 4 is pulling from a tiny corner of the training distribution. It has seen most of the web, and it doesn't need to see things often to talk about them. I've seen it successfully summarize the contents of obscure personal blogs, or of a very minor news story that was current for a week in 2009.
So it wouldn't surprise me if GPT 4 performs well on tasks that are mentioned on a half dozen obscure web pages, or something like that.