Why can't I apply for a domain name myself?

In the domain name registration form, sections 7 and 8 ask you to provide the hostname and Net address of a primary server and at least one secondary server. They are not just PCs or Macs with a dial-up connection to the Internet. They are typically UNIX machines connected to the Internet full-time via high speed digital connections such as ours. Only organizations that already have such hardware and connectivity resources are qualified to apply for domain names (for others). The official requirements are further quoted below:
At least two independent Servers MUST be provided for translating names to addresses for Hosts in the Domain. A Domain name may be removed from the InterNIC database, after notice, if at least two Name Servers are not reachable and functioning properly.
DO NOT list Name Servers if you do not have permission from the owner to do so. Listing Name Servers without the explicit approval of the owners is not only unethical, but can cause operational problems for the Name Servers listed.
The Servers should be in physically separate locations and on different networks, if possible. The Servers should be active and respond to Domain Name System (DNS) queries BEFORE this application is submitted. Incomplete information in Sections 7 and 8 will result in a returned template. Most ISP's can provide one or more Name Servers if you do not have your own.
If you have trouble understanding the above text, then most likely you are not qualified to apply for a domain name on your own. The registration process contains a lot of behind the scenes computer software/hardware configurations. The process is not as simple as filling out and mailing in an application form.