Tactical Rock-Paper-Scissors in D&D/TTRPGs

[Duff]

Part of the problem with this kind of "RPS design" is that even when you can get the PCs to fit neatly into these categories, as you get to higher levels it applies to the monsters less and less. For example, what would you consider a Rakshasa to be - Fighter, Mage, or Thief? What about an Ancient Dragon? How about a Planetar? Or a Marut? Or a Death Knight?

This can be a problem or a feature.
If you want to design a dragon that is equally dangerous for all the classes, that's fine. It doesn't matter whether the party are all theives or if they're a mix. And I'd call that a strength because a dragon is always dangerous to all parties.

The idea that other monsters are more or less skewed toward the center or the different corners of the RPS triangle is part of the diversity. The GM needs to consider that their mage BBG is going to be very tough work for the party of all fighters and maybe they get great value from recruiting a thief for this mission.

Other classes not occupying a corner also doesn't have to be a problem. If one player's druid character turns into a bear and fights like a fighter, or stays human and fights like a mage, that's fine, as long as the game design understands that that flexibility should be coming at a cost and the GM understands that they need to take that into account when planning encounters

If you like this R-P-S interplay, you could even build in several. Ranged-heavy-light. Religious-Arcane-Psionic Wolf-eagle-rat earth-wind-fire-water

At the cost of drastically slowing down action resolution. Because now everything's an opposed "check" of some type. And that's super ultra slow once you have more than just a few combatants. Because instead of being able to roll 20 attacks at once and counting successes, I have to do the whole thing individually for each pair.

Even if the targets all have different ACs, unless you're making all your attacks on the one target, you have to individually roll.
Even if you're attacking the same target, unless there's no chance you're going to want to switch targets after killing (or putting an effect on) target 1 you're going to roll them individually.
So this is less of a change than you might think