Here in Researchgate, I have seen many people sharing reviewers comments and author's response documents. Sharing these documents might help especially if someone want to learn what were the questions and comments raised by the reviewers and how the author responded to the reviewers comments. This is helpful especially to students who are new in scientific publication. It is also helpful to improve transparency in science.
However, the issue of authorship remains unclear in these documents. The reviewers comments is written by the reviewers not by the authors and I feel the author should not take credit for it. But if the author still wants to share it, I suggest tagging the reviewers with the document is important. Any opinion? In many open access journals who use open peer review policy, there is a possibility to know who the reviewers were at least when the paper is published.