Forrest McDaniel explains that TANSTAAFL:
Let me share the conclusion now: included columns in an index always get included in the log record, even if they weren’t modified. The same is not true for the clustered index. This can really matter if log generation is important to your environment, e.g. using an AG.
Click through for the proof. We often think of included columns on indexes as being nearly free performance gains, but “nearly” is carrying a bit of water here. This shouldn’t dissuade you from using included columns on indexes, but is a valid reason not to include all 50 non-index columns in a table “just in case.”