In the modern academic practice, the question of where a particular idea came from, or whether an axiom is ontologically correct, is considered vacuous and out of scope. For the most part, you’re just handed a rulebook to play someone else’s game.

To be clear I think the standard intuitive semi-naive set theory is the correct approach for most math students. But it didn't work for me. I needed to see the axioms and formal language.

Have things changed? Last century, this was a key part of (in the US) high school geometry courses. I won't argue that it was as in depth as you'd get in a college course (like you'd be exposed to in a math or philosophy degree program), but it was formal logic and it was taught.

is equivalent to "Do finish the house chores, or you can't play Minecraft".