The opening and closing themes for an anime are very important for quickly establishing the series’ identity to the viewers. This is why anime studios will usually team up with a major record label to get a hot artist to create a song for the opening, closings or insert songs.
But you might be surprised that some series have broken out of the traditional route using English songs as the anime theme. Not just indie bands, but world famous bands like Oasis, Duran Duran, Radiohead, and Backstreet Boys have lent their songs to anime. Yes, Backstreet Boys and anime.
The English songs done by the big name bands tend to be exclusive to Japan, Some anime licensors might be able to get such songs for one episode, but often times they will have an “international” song done in Japanese for their release. English language songs by Japanese groups tend to be internationally licensed.