Celebrities don't use new media to their advantage?

One of the reasons for Elvis' fame was that he was relatable to teenagers who until that point just followed their parents, The Beatles were so massively popular because they tore down the celebrity establishment and were seen as more relatable. It only makes sense that celebrities could raise themselves to the same level as Elvis or The Beatles by making themselves as relatable to normal people as those artists were able to.

Social Media seems like a perfect way to connect with fans in the same way that they would connect with any other person, why is it that no celebrities (with the exception, maybe of Lady GaGa) have used social media to it's full potential?