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Aside from the added/removed resistances/weaknesses proposals (which I seem to share with most of this thread), here's a second proposal: rearrange them in a circle:
Fire > Bug > Grass > Ground > Electric > Flying > Fighting > Rock > Ice > Water > Poison > Fairy > Dragon > Steel > Psychic > Ghost > Fire
Normal and Dark are pure neutral types now, none of them are weak to any type, but they don't have resistances either, nor are they SE against anything (it would be super good if there was a Light type right now so that it could form a pair of its own, Dark > Light --> Light > Dark, but I digress).
Some notes
>breaks the WFG core, but couldn't think of other ways to include some types like Bug
> super effectiveness is clockwise and resitances are counterclockwise
>Fairy can't be taken out of the circle to form the pair with Dark, since Dragon is SE againts Steel because of fire breathing and Poison resisting Dragon would make sense
>Ghost is SE againts Fire because of the ability of spirits to lower temperatures
> Steel is SE againts Psychic because Steel also represents technology here, so it's a "science beating superstition" scenario here
Weird idea, but felt the need to write it down.