We have a few questions and answers about when one would prefer a biased estimate over a unbiased one, but I have not found anything on the reverse question:

In what situations is it important to consider only unbiased estimators?

A lot of emphasis is put on the concept of unbiasedness is introductory statistical courses, but I've never read a compelling defense of this. Since we generally only collect data once, when is it useful to be correct on average (besides the possible psychological comfort it provides)? In what situations would one need to be correct on average?

I'm open to philosophical arguments, but would prefer concrete examples from research or industry.