Why don't we use Manhattan distance instead of euclidean distance in linear regression?
The main reason for that may be typically use Euclidean metric; Manhattan may be appropriate if different dimensions are not comparable.. While using regression-based methods you may have noticed that you usually have features of real values. You usually normalise the features and feed them to your model. The act of normalising features somehow means your features are comparable. In cases where you have categorical features, you may want to use decision trees, but I've never seen people have interest in Manhattan distance but based on answers [2, 3] there are some use cases for Manhattan too. You can also consider that they are comparable.