Over the past 14 years, I've purchased quite a few books and CDs from Amazon. But I've never gotten an email from Jamie Oliver or Martha Stewart or Martina McBride (some of these were gifts).
That seems like a huge missed opportunity. I don't mean a generic email from Amazon telling me that so-and-so has a new book or CD out, but right after I purchase, why not an email inviting me to join their fan club on Amazon and their mailing list through Amazon. Does Amazon even have fan clubs on its site? Even if it's just an enhanced author/artist page curated by the artist or their management, you'd think anything that gets people to come back to Amazon on a regular basis, even when they're not specifically intending to purchase, would be a good way to (let's face it) sell more.
And on the email side, that would open up a way for the artist to reach a portion of their audience who might never visit a fan site, never otherwise sign up for a newsletter, and turn them into a more engaged fan with a deeper connection to the artist.
For some artists, that might be all they need, they might not need a separate website. As we see Amazon starting to produce its own books and Netflix producing its own shows, this could help Amazon get in the door on special performances for musical artists. Could also help turn artists into fans who go out of their way to encourage their patrons to buy their offerings through Amazon.