Bucketing is usually used in industry because we are not sure what we are going to get. Some amount of observation on the distribution will give you a good idea of bucketing. But, there is caveat, if there isn't a lot of variance then bucketing won't help much.
Also, in terms of losses, since different buckets will have different number of examples, class ...
Answers in the comments are decent, particularly DuttA.
DuttA gives these, approximately
ease of derivative
Don't have to worry about ~0 in denominator causing huge gradient
But to me the most important is mathematical convenience, someone
might easily make the mistake of RMSE is just equal the difference
y−y′ instead of root of mean square of y−y′. The ...