Why is it that the necessity for balanced data sets is (almost) always exclusively mentioned in the context of classification but not of regression?
Balanced data sets are important in regression. Especially for accurate predictions through out the space. If the data is skewed towards one end of the distributions, predictions might be overly weighted to that region. This can cause problems if future data does not follow the same distribution.
One possible reason unbalanced data is less well covered in regression is because it is not assumption of the modeling fitting process and often the hold-data set is often part of the same batch as the training dataset. It can become an issue if a regression model goes in production and the data distribution changes.