I'm not sure where this idea of domain names being infinite came from, but it isn't really true[1]. There is a maximum length per top level domain, and also a finite number of top level domains. Until we're allowed to register top level domains, it's going to stay this way. Even then, we will be limited by the maximum allowable characters.
It doesn't matter how you get the limited resource first. What matters is whether there is an efficient trading system for such resource. You can always buy a domain name from someone you want if you are willing to pay big bucks.