I'm studying K-means, and one important drawback of K-means is the lack of robustness to outliers. My question is: are there any cases when the lack of robustness to outliers may be considered not as a defect of K-means but as a virtue instead?
yes, in detecting abnormal cases.
In the k-means based outlier detection technique, the data are partitioned into k groups by assigning them to the closest cluster centers.
Once assigned we can compute the distance or dissimilarity between each object and its cluster center, and pick those with largest distances as outliers.
The answer to you question is yes. K-means can be used as outlier detection. BUT, more attention needs to be given for the definition of outliers. In K-means, using the symmetric distance measure is the key component to define the samples that belonging to the same cluster. symmetric distance measurement gives similar weight to each dimension (feature) this may not always be the case for defining outliers.