This doesn't seem quite right to me:

  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.

I very much had the opposite problem with Munkres's Topology or Dummit and Foote's Abstract Algebra: those authors hand you the ontological / scientific justifications for "everyday" ZFC without actually telling you the precise rules. I had to read a formal book on mathematical logic before I really understood point-set topology (at which point my misconceptions were clearly trivial confusion).

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.