Since most spam is so obvious, multiple reports aren’t needed, so no sense in burdening other posters and indicating something has been reported accomplishes that. And since there is little doubt as to spam, publicly indicating a post has been reported is welcome. In other cases that are not spam, depending on context, it could be seen as a form of junior modding. In this instance it’s really not even close to an issue, so no big deal at all.
In general, private reports are preferable because of the aforementioned potential of junior modding, and also to avoid the potential disagreement with the report. There is also the potential back and forth between posters saying they are reporting each other’s posts.