Reducing Regression to Classification
No, minimizing the classification loss does not translate to minimizing regression error and does not yield better regression performance.

This is a core tenant of Measure Theory. Regression measures outcome variables on ratio, interval, or ordinal scales. Classification measures outcome variables on nominal scales. You can always go from more complex scales (i.e., ratio, interval, or ordinal) to simpler scales (i.e., nominal). There are no guarantees about going back. This is technically called a non-injective mapping.

One way to think of it is that you are picking a downsampling scheme to map the data from regression to classification, and there are many possible mappings back from classification to regression. There are no guarantees on which mapping was used. Once downsampled, the data has to stay in the lower sampling space.