Well, even before that became a standard practice, quite a few anime theme songs in Japan were basically based on more intangible things than "This is the show, these are the characters, this is the premise, Doh wah" . While Dragon Ball, Kinnikuman, and a few others that escape me at the moment basically follw a more western sense of theme songs, there were some others (I just can't think up now) that were basically about feelings and the like vaugely related to the show's premise. This is beneficial to both the show (for people who are fans of the band, who want to watch the opening/closing, and buy the soundtrack/single), and the band (for people who are fans of the show, finding out about these bands they normally wouldn't get exposure to).
So far, the only times a band performs the theme song, it's a show about the band- Puffy's show, Weird Al's show (granted, it was livce action, but still apt). But then again, Warners tried this as an experiment, getting 2 bands to perform cartoon theme songs. Chicos de Barrio- Mucha Lucha, and A Simple Plan- What's new Scooby Doo?
Sadly, there are big markets for animated theme song soundtracks outside the US. Japan for one, and France pretty much released lots of soundtracks of the French versions of theme songs, especially to American and Japanese cartoons. There's a site I know where you can listen to the French ones (but not download them), and I don't know if that's okay here, so if you're really curious, I'll tell you privately.