Despite being boosted by Dave Chappelle (and doing a good guest shot at a Buddy Guy show I saw), you might not care much about John Mayer but I found it kind of interesting that he was opting outta Twitter. He's not the first and won't be the last star to do it.
What's really interesting is what this means for fans though. On one level, you could say that it's a canny publicity stunt (it worked not just here but also had write-up's in articles like this one from The Wrap). Remember also that Trent Reznor got fed up with some of his followers who were dogging him on Twitter, kissing it off but later coming back to it. Similarly, Soulja Boy got mad at people poking fun at him and split the service, only to return later. Also recently, Miley Cyrus decided to deprive the world of her 140 character or less wisdom, also taking down her Twitter account but unlike Soulja or Trent, she's stuck to her guns and hasn't rejoined the service (at least so far).
As the Wrap article points out, if you really miss Mayer, you can still find him on Tumblr and similarly, these artists have plenty of other social media outlets like Facebook to reach their fans (MySpace too but less and less nowadays). Fans themselves aren't necessarily tied to Twitter alone either so that they don't have to feel that their favorite musician is necessarily abandoning though some of 'em will be hurt to see them go.
Why jump the ship with Twitter though? Maybe it has something to do with the nature of the service. Because it's so personalized (as Miley complained) and because you can get immediate feedback that ain't always complimentary (as Trent and Soulja complained), it's not ideal for every musician. Twitter is a good way to get the word out about your work (album, tour, etc) but as these artists find out, mingling with their fans can be kind of thorny sometimes. Or if you wanna be less charitable, you could also say that these artists are just too damn thin-skinned for their profession.
For musicians I follow on Twitter, I'm not so much interested in news they're spreading or peddling (which you can always read elsewhere in more detail) but something more personalized, as Miley fears- seeing what makes them tick and what they have to say about their lives and what they encounter there. That's why I like posts from Weird Al and Kanye West and Questlove. They might not be as weird or funny or enlightening as they think but if you're curious at all about them, they reward the attention for sure and give us a small piece of themselves. And in the end, ain't that what we want out of the artists we love?