You are right, elemental grudges are exactly what you would expect. But the game isn't made like that. I would also expect the creatures to fight. Instead they directly attack the opponent's HP. Like a rugby player scoring a point while a player of the other team is simply standing in front of him. It doesn't make much sense, but that is the game.
I have not seen a single bit of argumentation that suggests this leads to a meta game problem. There are 12 elements. Every element would get a small bonus against just 1 other element. So, in some games you'd win more often, while otherwise you'd lose more. Makes no netto difference. Also, the division needs to be asymmetrical. A
and
grudge is nonsensical, as the results would nullify each other.
In the end, I think this is very much possible, but I wonder if it makes any difference overall.