First, I don't like easing American control over the Internet, and neither should any free citizen of any nationality.
However, there is nothing magic about DNS besides consensus, and there isn't much of a mothership database. DNS data is highly distributed across millions of individual DNS servers.
A dozen or so root name servers are all there is to the centralized part of DNS, and they are running software anyone can download for free. The root name servers don't really do anything different from the local name server in your office, or at your ISP.
Domain names are read right-to-left, and there is an invisible dot at the right hand side. So, you search for
www.texaschlforum.com. (even if you don't put the dot in, it's hypothetically there). "Dot" is the root DNS zone.
Your machine asks one of the DNS servers it's been told about, probably at your ISP, for
www.texaschlforum.com.
If the ISP's DNS server has just been booted up, it doesn't have a clue where that is, so it refers to a static list of name servers it knows about, likely listed in a file called named.cache, and asks where to find "com".
The root name servers (actually whichever one your ISP's DNS server decided to ask) gets referred to a list of name servers for .com sites.
Next it asks the .com DNS servers for texaschlforum, and follows a reference to the authoritative name servers for texaschlforum.com, which return the IP address for
www.texaschlforum.com. Your ISP's DNS machine will also remember the result for a while. Each DNS entry (zone, actually) advertises how long addresses should be remembered. That's unenforceable, but it's a nice convention.
It is trivial to set up your own root name server. The trick to getting it to be of any good would be ISP's listing your new root name servers in their named.cache files. I've often thought we should have widely available shadow DNS systems.
It wouldn't be hard, other than getting everyone to agree on what to use.