Yes, but no.
I think what people are really looking for is some kind of software platform that allows them to put up their own website, so nobody else can delete it out from under them, but also have some kind of interaction with other people with their own independent sites.
So that they can press a button and "retweet" something someone else said, or reply to it without creating a new account on the site of everybody you want to reply to etc.
The hard problem is probably to get some kind of a distributed user accounts database, so that you own your account based on cryptography rather than the capricious whims of billionaires, but still use it on more than your own website. Maybe something like Namecoin but for usernames.