Citations Needed had a mini series where they discussed why this happened. The US government will give material support to movie and game studios in exchange for some creative control over the content. That’s why so many movies with military equipment in it are rabidly pro-war; the studios don’t get access to the real equipment without the government’s support, and they don’t sign off on extremely critical scripts.
COD and similar games don’t just pop out of a void and still strive for some semblance of realism. That is a huge selling point after all. So the government gets involved, even if in little ways. Same way China gets to censor movies, either by omission or fundamentally changing things, around the world.