Since I've seen people manage to re-implement cursors (in all there varied forms) using other TSQL constructs (usually involving at least one while loop), there's nothing that cursors can achieve that can't be done using other constructs.
That's not to say that the re-implementations aren't equally as inefficient as the cursors that were avoided by not including the word "cursor" in that solution. Some people seem to purely hate the word, not the mechanics.
One place I've successfully argued to keep cursors was for a data transfer/transform between two different databases (we were dealing with clients here). Whilst we could have implemented this transfer in a set based manner (indeed, we previously had), there was problematic data that could cause issues for a few clients. In a set based solution, we had either to:
- Continue the transfer, excluding failed client data at each table, leaving those clients partially transferred, or,
- abort the entire batch
Whereas, by making the unit of transfer the individual client (using a cursor to select each client), we could make each client's transfer between the systems either work fully or be entirely rolled back (i.e. place each transfer in its own transaction)
I can't think of any situations where I've wanted to use a cursor below the "top level" of such transfers though (e.g. selecting which client to transfer next)