First off, let’s remember the difference between clustered & nonclustered indexes
The clustered index is organized by the key columns. It also includes every other column as part of the row structure (ie, it has the entire row).
The nonclustered index is also organized by the key columns. It implicitly includes the clustering key columns (if the table is clustered), or a pointer to the row (if the table’s a heap). If any
INCLUDEcolumns are explicitly specified, they will also be included in the index structure (but these included columns don’t affect order).
I’ve seen other cases where it made sense on sufficiently large and wide tables even for seeks (where the page density difference is large enough that you have a 4-level clustered index but a 3-level non-clustered index), so I think there’s more than Andy’s one corner case. But I do agree that it generally doesn’t help.