There are a few times where Cap steps down because he’s so disgusted with what the U.S. has become. I’m not super familiar with them, but he became Nomad at one point.

In the comic run of Civil War, everyone expected Cap to side with the government, but he refused. The government then proceeded to build a prison/concentration camp for super powered individuals who refused to comply… It’s been a while since I’ve read that arc.

Hydra got the WH

You should watch the Winter Soldier film.

Check out the comics. There’s plenty of stories about literally what you’re asking.