The most stark example against this is the original MW2 - in addition to the anti-war quotes everyone loves to talk about every time you die, the main antagonist is literally a US Army General (admittedly he is distanced from the actual Army by the end, using a PMC instead).
The black ops games have some twist that often provoke the the thought of whether the ends justify the means. ::: In Cold War, the main character, Bell, is actually a captured Russian soldier that they have brainwashed to fight for the US as part of an experimental program. When this is revealed, you have the option to betray your “team” and lead them into a Russian trap :::
That being said, I haven’t played all of the cod campaigns, especially some of the more “historical” entries. It’s more fun to play this type of game when it makes you feel like what you’re doing is justified. It’s important to remember it’s all fiction, but hey, it’s not going to be for everyone. If you feel like the game you’re playing goes against your morals, no shame in switching it off for something else.
As Reggie from Nintendo once said, “If it isn’t fun, why bother.”