For 5E, the core problem is simple: it's not the design goal. 5E is specifically designed to be simple; whereas emergent RPS requires lots of complexity and choices.
It's not surprising you don't see much tactics in 5e; as not everyone wants a highly tactical and complex wargame.

There's also a big decision problem: RPS depends on both sides making decisions. But the DM has a lot more decisions to make, unless monsters have somehow automated attack routines; it's also harder to setup good systems that have information hidden from the DM, and hidden information is often a key part of RPS systems.

The nature of upgrade systems also presents a challenge; it's hard to have upgrades uniformly affect all parts of a character. There also inherently tends to be choice in builds; that is, people choose how to build their characters. Thus, even if the system is carefully balanced and designed so that flexibility is more optimal; some players will simply choose to build a character that does one thing very well. If one player simply built to always do rock, then there isn't a lot of choice, rock either works or it doesn't. 3e has a fair bit of this; in that some stronger builds are often based on picking one thing and doing it very effectively. counter-counter-measures exist. So instead of trying to do every type of thing, you take abilities that counter your counters, so you can stick to your core strategy. Ofc 3e also has the problem that some abilities are so broad that it's not so much rock/paper/scissors as rock/paper/scissors/nuclear bomb.


Thinking of how others game handle this; some videogames occur to me, which presents the challenge that what works well in a videogame is quite different from what works well in a TTRPG. In part simply due to how many dice/rolls and units are involved.

The dominions series has lots of complexity and various interactions that lead to certain units being good/bad against others; and it could be adapted into an rpg, though I'm not sure those interactions would work well there, as part of the complexity comes from having so many units to choose from. There's also the inherent warfare choices of how much to commit to each theater/where and when. Whereas in an RPG it's typically more 'this is the battle'.

Poker Quest RPG (a small indie videogame) has a number of emergent counters, though they do tend to fall into certain clusters. The basics of the game is it's you vs 1 monster at a time; and it uses a deck of playing cards with no duplicates. Each round the deck is shuffled and the players gets some cards, and the monster gets a mix of face up and face down cards. Each monster has a variety of attacks/abilities it may use (in a deterministic order) based on what cards it gets, note that the amount of cards 'spent' on an ability can be anything from 0 up. Some monster abilities require specific comboes the monster is unlikely to get, but are powerful when they do (eg requires a full house, or a black jack), against such monsters expensive abilities that let you manipulate their hand are quite effective. There are other monsters who have lots of hidden cards, or who have abilities that are'nt that dependent on the particular cards, against whom hand manipulation is less effective. Damage block abilities are strong vs monsters that are predictable, but less so against some others. Ofc a good portion of the strategy in the game is choosing the path to take, so that you fight monsters that your char does better against, as well as factoring in the many tradeoffs along each path. Something which doesn't tend to translate to TTRPGs where the set of foes to face is usually much more set.

Combat as war doesn't mesh well with RPS gameplay; because the core rule of combat as war is that you don't fight RPS fights, you only fight when you're going to win, if at all possible.