Unfortunately there is no halfway with maths. Math is the language of logic, the purpose of mathematical formalism is to allow easy communication, not just naval gazing.
This is half right: you don't learn math by reading proofs, you learn it by writing proofs. Developing strong intuition without proofs is possible (albeit difficult) for applied topics, but not viable at all for pure math.
It's only supposed to be somewhat intuitive for those who already possess some intermediate level college math background.
And no, rejecting the notion that not every advanced topic is supposed to be accurately ELI5-ed with a cringy Redditesque tone, means neither there's any gatekeeping taking place nor there's lack of understanding from the potential explainer's side.
But I've seen both it and the alternative. It is literally easier to learn the math, and then use that to facilitate communication, than to attempt to directly communicate key concepts while avoiding the math.