This is a problem because apparently in the States there are certain laws that require all captions intended for the hearing-impaired to match what a hearing audience would understand. Which pretty much means that if there are lyrics, they need to be included. Some studios still don't do this, and they're flirting with problems with the law.

Note that subtitles *not* intended for the hearing-impaired (intended, for example, for foreign audiences) don't need to have songs included, and most don't.

But when it comes to subtitles for the deaf and hard-of-hearing, you need to have lyrics.