"What a new Internet might look like is still widely debated, but one alternative would, in effect, create a “gated community” where users would give up their anonymity and certain freedoms in return for safety. Today that is already the case for many corporate and government Internet users. As a new and more secure network becomes widely adopted, the current Internet might end up as the bad neighborhood of cyberspace. You would enter at your own risk and keep an eye over your shoulder while you were there." -John Markoff, Do We Need a New Internet?, New York Times, 14 Feb. 2009
The drive for a new Internet and a move into an online "gated community" reminds me of the post-WWII "white flight" from the urban areas and the inflated perception of urban areas as wastelands. And later, the suburban areas started becoming more dangerous as the decades progressed, and the residents built sprawling ex-urban neighborhood (i.e. Irvine) in order to continue escaping the crime. However, because people continued to run away from their cities' problems, they haven't dealt with the crime directly, and the urban areas have been neglected because of it.
I know I'm generalizing with the above example, but I don't think a clean slate for the Internet will necessarily solve our problems of viruses and hackers. A "new Internet" would not completely eradicate our problems because the problems will continue ruining the "old Internet", and that would be a very irresponsible decision that affects users who would not be able to access the "new Internet". Also, more problems will be invented later, and the clean slate won't last forever (law of entropy).
I honestly believe that we are as safe in the virtual world as in the actual world (as in, absolute security is never guaranteed). And sometimes we just have to take problems as they come. I think we'll come out better by taking back the Internets.