Why we have to buy Domain Names?Koeln, )
The rooting of a domain name is only working, if the domain name (your name+top level extension) is unique.
You cannot establish and administrate the DNS system as an indivudual. You can compare the complexity and size of the DNS System e.g. to the US postal system.
Registries and Registrars collect money from many individuals to build the capital in order to finance the technical system of the DNS System.