The journal that invited me recently to review a submitted paper doesn't have the practice to inform me about the final decision regarding papers I reviewed. So far, this is my third review for them and for the previous two, I didn't get any feedback. As an example, I suggested a major revision and after a couple of weeks I received the revised paper, then I suggested a minor revision and had radio silence since then (6-7 months ago), so I have no idea whether the paper was accepted, rejected or withdrawn.
Are there any reasons why the details of a peer review process should be kept secret from the reviewers?
I see two levels of consideration to this question. The first is just to inform the reviewer about the decision and the second is to share the complete "public" review correspondence with reviewers. I really fail to see any damage that could occur.
As for my motivation, there is of course the closure of the invested reviewing effort and there is also the feedback whether or not my review was on par with the others (both by recommendations and by comments), which would benefit me in future reviews.
EDIT By "public" I mean the same information that is shared with the authors, specifically the decision at the stage and possibly the comments of the other reviews directed at the authors. The process is not double-blind, so no new revelations are made, the authors remain known, while the reviewers remain anonymous.