Well, I think the title question pretty much states my question. The reason I think there might still be value in using such estimators is that estimation often happens with parameters that were, themselves, estimated. Furthermore, the model in use is often known never to be a perfect fit, in spite of the fact that is the best parametric model that could be found.

I have experience with biased estimators being useful, but not with different unbiased estimators - especially when one of them is theoretically optimal.