Could celebrities kill the media obsessed with them?

John Cleese, on Twitter (it is apparently the John Cleese), has two comments on a Daily Mail article about celebrities using Twiter, he says:

Daily Mail Cottons onto Twitter Shock! they of course hate the fact we chat and interact without them, don’t they?

And, adds:

The thing is that the press and trad media have had a virtual monopoly for a long time.. it must hurt them to see it vanishing pfffffffft!!

Blogging (Cleese also has a blog) and having your own domain name has been already been mentioned for years as a way of any famous person or business person, or businesses,  to have a direct public reach. But is it wishful thinking that celebrities them selves could seriously harm the red tops, magazines and blogs which are obsessed with celebrities? Or could it make them even more aggressive and (subjectively) distasteful?