Question: Why do domain registrars require two name servers?
Answer: The short answer to this question is that Internet standards require it according on RFC 1034, published by the Internet Engineering Task Force (IETF). But there is a good reason for it.
The intent of the standard is to ensure that domain name servers have redundancy. If one name server goes down, a website will still have at least one more to keep it alive. In other words, your server could be working perfectly fine, but without name servers, no one will see your site. Furthermore, sites with heavy loads might be able to distribute that load between the two name servers.
Because of the above reasons, the intent is to have two distinct name servers, at two locations, using two different IP addresses. If you have your own server and do not have access to a another server for DNS, I recommend using one of the many DNS services that are available at low cost. It will save you trouble in the long run and will make sure your site is up to standards.