I’m with you except for 2. Knowing math is great.
But ask me to do subtraction? Forget it.
20 year programming career and I've never engaged with math beyond approximately Algebra II, in the real world. Hell, I go years at a time not needing anything trickier than Algebra I.
Nearly all of the math I actually use I learned in the 6th grade or earlier, overwhelmingly elementary school arithmetic—mostly the "bad" kind I got from memorization-based practice that mathematicians seem to hate even though it's a contender for the best bang-for-buck of almost my entire educational career, plus a lot of fractions-related stuff (so, so very many people are terrible at this, can't even do basic things, IME it's where an awful lot of people permanently fall off the math-train, way back in like 3rd grade), basic arithmetic, and pre-algebra-tier simple variable substitution.
Every now and then I get a bug up my ass to try to expand my math abilities, but 1) I'm so goddamn rusty at this point because I never use any of it that I have to start back at brushing up on high school stuff, which is discouraging, and 2) I'm not even really sure what I'm going to do with it (long experience suggests: nothing) so the motivation fades fast.
Weirdly my math background is actually more useful as a 'soft' skill in my current work. I am the go to person for talking to the data analysts in my company, and having a statistics background is pretty helpful for interfacing with managers or people outside the dev department.
Every once in a while I remember an algorithm for doing something I can include in our app and feel like a God, lol.
I can distinctly remember the three times this happened for a team I was on, in my couple decades of doing this, because everyone involved kinda got a thrill out of the extreme novelty of doing something resembling actual math of even a lower-end-of-undergrad level. Lasted all of a few minutes to perhaps a few hours, but still.
It's not the math facts you learn so much as getting lots of practice with that kind of reasoning.
It contains lots and lots of exercises.
This "well actually you're doing math!" stuff feels like some kind of rhetorical trick, when the "math" I'm doing doesn't seem strongly related to or to require being any good at the math-thing it supposedly is. It's not quite the same thing nor quite so far off the mark, but it seems at least in the same ballpark (ha, ha) as claiming that professional sports players use lots and lots of complicated trigonometry. Sort-of yes, going by something like unfair riddle-logic, I guess? But in reality, no, of course they don't.
I don't see any daylight between this claim and, "diagnosing a funny noise in an engine is math," and if that's true then I think we're heading into territory where we've rendered the term "math" so broad that it's no longer useful.
It's maths in the same way as when your brain hears a note at 440 hz and you go 'that's a C', i.e. while it may be practiced, the maths part of that is subconscious and its completely detached from the conscious maths anybody except mathematicians think about.
In the case of catching a fly ball, the "thinking about" approach using trigonometry is completely unhelpful. In the case of music, the "thinking about" approach of theory can be helpful, but many people who learned informally have been brilliant musicians without ever learning a formal approach to theory. In the case of math, the critical "thinking about" aspect is vital. Pretty much everybody needs it, Ramanujan aside.
What unites all of these cases, however, is that the formal "thinking about" aspect is useless on its own. Without the productive, creative aspect, it doesn't have anything to critique and make better.