Vicki, I'd go further and say that we don't really have much special personal connection to any of our relatives, poor or rich, once you get back 200 years or more. My interest in searching back so far is mainly because it is a way of studying history.
Whenever it is actually possible to find connections between less famous people it can be more interesting than studying the connections of famous people. HOWEVER, the famous people appear in more records and are better studied, and so studying their connections is often a great starting point for studying the connections of all the less known well-known people.
Having a connection to Edward III does not make you special. It is quite common. However, studying all the steps in that connection is a great way to learn about how families changed over time.