Completeness vs. consistency

In the early days of my programming career I was obsessed with completeness of the API's I was constructing. Of course, over the years I learned better, than to waste my time. But I still couldn't construct a clear cut argument against complete API's. Aside from the time constraint issues, "complete" certainly sounds better, than "incomplete". That is before I read the Gödel's Proof. The fog has cleared (but my math is still rusty at best, so I could be blowing smoke, for all I know). Clearly (please do correct me if I am wrong), any given software system is a formal axiomatic system and as such, it is essentially incomplete. So there we go, from now on I don't feel guilty concentrating my efforts on consistency instead of completeness.