Hmm... I can't see that being terribly useful. I think having it there as a default would be a distraction.
If anything, should be a button or something for "use my ip address". But I imagine the 95% use case being people with cloud servers, not trying to get a hostname for thier current computer's ip address.
What's wrong with leaving a default in there being your current IP? I think you're wrong in your assumption that people want to use something as transient as this for a server. If you have a server, you probably have a domain.
This is a great service for assigning a name to your home or office router and then using that for NATting in.