In single-blind peer-review, can you reveal your identity without the editor's consent?
I would think that it's a bad idea to open the possibility of referees communicating with authors, since this opens the possibility of authors' influencing referees, compromising the process. Of course, this is not to say that there aren't some positive possibilities, but the conflict-of-interest criterion seems to me in this case to be clearly manifest.

That is, it should be understood, implicitly or explicitly, that referees will remain anonymous "in perpetuity", so that there is no hint or possibility that authors could communicate with them or influence them. E.g., either overt or subtle invitations from authors to a referee to communicate (and get some credit for the paper, maybe co-authorship, etc., as discussed around here some time back...) would be understood in advance to fail absolutely.

Thus, editors who discover referees willing to engage in such would probably regretfully stop asking them to referee, since if such activity became known it would seriously damage the reputation of the journal... if only in principle, but "principle" would seem to be the point...