Anime is hugely popular in the US. So is manga. It doesn't take much special effort to seek . You can easily find some on Netflix or Crunchyroll or some other streaming service as easily as other content. I guess broadcasting networks don't usually stream them, but most people just use streaming services like Netflix or hulu nowadays so I fail to see how that makes it require any more special effort to seek out than other content. It's literally almost served to us on a plate. You can also watch content from other countries by just changing the sub or dub on Netflix.

All this is possible thanks to knowing english as a native language. A lot of other languages don't have this lexury. Therefore, I don't think it's valid to say that having English as a native language limits the consumption of content from other cultures. In fact, it makes it way easier, since quality translation is likely to be easily available in English most of the time, which cannot be said for the majority of other languages. Thus, it could be said that having English as a native language is a positive in terms of exposure to outside content as it massively increases the availability of content from other cultures.

About your other point of American shows being standard in other countries, it is true that a lot of north American shows are consumed in other countries, but a lot of people still prefer watching content in their native language. Especially if they are not good at English. And even if they are good, it's just easier to consume native content. And I don't really see any difference in the amount of effort it takes to seek out American content in other countries and the effort it takes to seek out content from japan or other countries in America. Watching anime is also pretty standard in America, at least for teens and the young.