In a wargame, each side usually has a lot of pieces of the board, like 10 or 20 or more. Things like range and movement speed and morale are important. And either side is supposed to have a reasonable shot at winning, albeit with losses.

In an RPG each player gets one piece, there's only like 4 players, and the DM probably isn't controlling 20 orcs either. Morale ge really isn't modeled at all, and the general trend towards activated player special abilities generally makes maneuver less important. Most importantly, the players are supposed to win, the monsters are just there to provide an enjoyable obstacle, meaning one that every player can contribute to overcoming.

These are not design considerations that favor RPS style balancing. If I'm playing an archer, I probably don't want every fight to consist of like 2 dudes I totally body, 2 dudes I'm indifferent against, and 2 dudes who absolutely wreck me given half a chance, because I'm gonna end up getting wrecked sooner rather than later. I want to be effective against, and durable against, most threats on the board, because that gives me the freedom to use my fun special abilities.

I think the modern tendency in RPGs away from harsh penalties for things like shooting a ranged weapon while threatened make it abundantly clear that nobody wants RPS balancing, precisely because it shuts down characters. It's right up there with throwing a beholder into every encounter, so that there's a counter to the wizard - the whole point of playing a wizard is you want to wizard things, not contend with intelligently employed anti-wizard assets all the time.