That's kind of what Handshake.org is trying to do, although instead of forking existing TLDs Handshake lets people register their own TLDs outside of the 1500 T

That's kind of what Handshake.org is trying to do, although instead of forking existing TLDs Handshake lets people register their own TLDs outside of the 1500 TLDs the ICANN has already provisioned. There have been many alternative root attempts in the past, but I think the only way for one to succeed is if it starts off by augmenting the existing system instead of making users choose between one or the other (that can come later).