If I understand correctly, that wouldn’t change things: hyphens are used in English to link words (e.g., “work-product privilege” — the noun work modifies the noun product, and the two together modify the noun privilege) but two linked nouns of equal importance are a special case.

(Not my intent to be pedantic.)

This is not the best source (I’m pressed for time) but it gives a decent explanation: https://editorsmanual.com/articles/en-dash/#elements-of-equa...

I have never heard of this role and I'm not aware of anyone who follows it. The document you linked says that it's only used "in certain styles". So it sounds like a stylistic choice that an editor may choose to use or not, rather than a rule to be followed everywhere.