Considering the information moderators see when other flags are used, why aren't they able to see who flagged a post as spam?
It would be helpful when there are many flags that need to be handled, and moderators want to first handle the most critical ones. If I see a post flagged by a user who keeps spam-flagging posts simply because they contain a link, or who keeps flagging posts without a good reason, I would handle the flags from that user as last step.
Probably, this is relevant on sites smaller than Stack Overflow. I saw what I considered spam posts only in few cases, on Stack Overflow, and I guess that most of the spam is not handled by moderators.
I recently saw a spam flag raised for a question that is not spam (the link is for 10k users on Drupal Answers).
If the flag was raised from a high reputation user, I could think the post was initially spam, but it has been edited not to contain spam links (or links that could be considered spam) during the grace period; in this case, I would keep an eye on the user who posted the answer/question. If the flag was raised from a low reputation user, I could think the flag was used by mistake (which could happen to a high reputation user, though), and I would not keep an eye on the user who wrote the post. Knowing who flagged the post doesn't change how I handle it, but help understanding if there is a possible problem.
If a user keeps flagging as spam something that is not spam, and the system doesn't stop her/him from flagging as spam any further post (in the same way a user who suggests consecutive edits that are rejected is not allowed to suggest edits for seven days), moderators should know who is that user, to take any necessary action.