My hot take is that math class doesn’t do the one thing that justifies its place in core curriculum

Does this even count as a hot take? Whether someone hates math and just thinks that because they don't want to do it or they love math and wince at seeing how much pain math classes cause, it seems there's a lot of agreement that the current system isn't great.

That’s kind of a pain in the ass, so what can we do?

Love that approach to math. Feeling like "I'm bored and want to be able to solve this question type without writing any work" and creating your own way to solve a problem that's very disconnected from the way teachers teach things. So frequently, the method taught are things that people can memorize for a single test, but without any underlying understanding, they won't remember a day longer. When they come back a decade from when they learned it, there's almost no chance they're gonna remember much.

Having real world problems you want to solve (not just wanting the answer, but wanting to go through the process) is also a nice way to start to learn the intuition of mathematical concepts. Playing Sonic is how I started to learn to think about infinite sequences back in elementary school. I didn't even know algebra, but I was thinking about things like questioning if a sequence would converge or diverge before I had that language to describe it or the tools explore it as much as I'd have liked to and trying to get an idea of whether it looked like the sequence was plateauing or growing infinitely by just doing calculations by hand. Didn't have a calculator to do such high-precision calculations nor did I know anyway to visualize the data.

there’s no reason anyone should be graduating high school with calculus under their belt.

I'd say that should be something some people should be exposed to to varying degrees. But its practically expected that you've taken such at competitive colleges, at least if you want to go into STEM.

PS: Is your username a Euler joke?