Domain names are needed because it's easier to remember say, microsoft.com than 207.46.197.32 or yahoo.com - 209.131.36.158
The registrars pay a fee to ICANN who coordinate the DNS servers. As well as the annual fee, around 20 - 25c goes to ICANN for each domain you register.
If you can remember lots of ip addresses then you've no need to use domain names, computers don't use them - just us humans. Typing 207.46.197.32 in your browser address bar gets you to the same place as typing Microsoft.com
Some people don't bother registering domain names and just use their server's IP address. However, as at least one person on Yahoo Answers found out, that doesn't make them private, it just means you need to know the IP address rather than remembering a domain name.

