How are trademarks registered? Why not use the same procedure for domain names?
In the case of Delta Airlines and Delta Faucets for example who would get to have "delta.com"? Then what about all the other countries with independent trademark rules and authorities?
I like the idea, but it would end up being way more complex than it seems.
You can append the country domain name, e.g. .us or .de, if you want.