Let’s say, the war in Vietnam 1965-1975 at the operational and strategic level.
I think this is a pretty good example of military operations being influenced by political considerations in Vietnam. In this particular case you have a Battalion of US infantry pretty much coordinating with South Vietnamese Police to lock down a suspected logistical base of the PLAF. That’s one battalion less in the field, which is a substantial force. If you don’t cover operations like that in some way, which is thematic and consistent with the rest of the gameplay, what you end up is with a weak tea game. Same thing, but coming from the other side, for COIN games that postulate themselves as “alternative” to wargames where more straightforward combat operations dominate gameplay.
What is missing, or hard to come by, is the testimony of the analogous operations ran by the Vietnamese Communist Party forces in South Vietnam. I am pretty sure that the BBQ at Ben Cui wasn’t the happiest meal ever had by the villagers, but I am also quite sure - looking at what Mao’s revolutionary handbook suggests - that the PLAF and the NLF were not known for their doctors or for handing out free barbecued pork belly meals.
For the most part… at the tactical level, where you would have to portray the actual face of war, no, not really. In that case, the appropiate format would be along the lines of Claude Lanzmann’s Shoah. Only that, in my opinion, would be respectful and proper. It would also be a very painful watch.
At a slightly higher level I do think game designers should portray these political constraints in some way, and could totally get away with it, provided it fits the theme of their games. For instance, operational games covering US forces in World War II should send a pretty stingy negative reward when losses are high. You don’t sacrifice the citizens of a democracy without paying a political post. Similarly, games covering the Nazi-Soviet war in the Eastern Front, that do not model the interference of the two “masterminds” at the top of the hierarchy on both sides, end up being a whitewash of hindsight and some pretty bland game outcomes.
One example of a game that gets away with the interplay of the political and the operational/strategic is, in my opinion, the best high-level operational wargame made in the last 25 years (better even than my beloved OCS)
and why is that? Because of this counter

That could be the name of a brand of eau de cologne in Indonesia, btw.
I am not going to steal Pat’s thunder, but what I have seen from his rules, I think he can totally get away with conveying political imperatives interfering with the conduct of military US operations in Vietnam, in a way that is both respectful with the subject matter, educational without insulting anyone’s intelligence, engaging as in thrilling, and thematic as in consistent with the scale and content of the game.