The problem is some governments would be perfectly happy with that. In fact for the most repressive ones it's long term goal.
China wants to create a separate internet for Chinese users and they're half way there. They have their own local censored versions of Google, Twitter and Facebook. Soon most internet users in China won't care if the rest of the internet disappears. Likewise for Iran, except they have been more open about it [1].
[1] http://online.wsj.com/article/SB1000142405274870488940457627...