Thing is, there are stereotypes everywhere. Film, television, musicals. They’re there. That’s not to say it’s right, but they are there. Lots of Hollywood films have British people as bad guys, for example. Does that stop us going to see the films? No, but it gets pretty boring.
Some stereotypes are actively harmful - as a disabled person I’ve come across more than one that people have tried to apply to me, and those who’ve tried to do so have ended up irritated or shocked when, guess what, I don’t meet their preconceived notions. I’ve had people telling me I ‘must’ be like this, because aren’t all disabled people?
The stereotyped Americans in LND are very stereotyped. But tbh, there are things that have a wider audience that have more harmful stereotypes. Take Glee, for example, which has a massive audience. Stereotyped gay guy, black woman, and disabled kid. None of the stereotypes there are particularly helpful, and can be quite harmful. But the world’s going to have to change an awful lot before we can get rid of stereotypes in film, stage and television.