First of all, let's be clear: the root servers are owned and operated by various entities in countries all around the world. The root zone file is the sole domain of the Department of Commerce of the United States of America. So you'd have to ignore all of them, and i'm not completely sure the US Government wouldn't force Google to apply the one correct root zone file (after all, Google is such a powerhouse you could complain of a monopoly of internet control or influence).
Potential legal issues aside, what you end up with is a New Internet. Of course routes all remain the same, but nobody refers to addresses or routes: they use host names. Thus you run a huge risk of networked applications just not working, which would affect everything from entertainment to commerce to government services and god knows what else (what if medical devices in hospitals needed to retrieve a firmware upgrade and couldn't connect to the right host?).
In practice there would be no technical hurdle to do this. It's simple to just configure your domain name server to include some records, leave out some records and change others. Some people do this if their ISP redirects failed lookups to some advertising-laden homepage, for example. But on a large scale, the modification of the naming system to one's personal tastes has broad-reaching negative consequences related to availability of hosts and the functional and legal consequences therein. On a personal scale (modifying only your own name server results), you get to connect to your poker site again. I prefer the latter solution. If operating systems just started including a simple GUI to modify their personal domain name caches we probably wouldn't need an alternate dns root.