The Response to Reviewers (RTR) constitute a crucial component of the research study that never comes out. Since, it comprises diverse queries of the peer reviewers, it may enhance the impact of study for the readers across the discipline.
In an open review process, the reviewers' question and your answers are open for discussion. But in a blind and closed review process, I hope you can not do this. I have not seen any journal stating about this clause in their "Guideline to the Authors".
I do agree with you that your response to the reviewer constitutes an integral part of your work, and that forms the backbone for the conclusions that you make in your research article. As the length of research articles are limited, it won't be possible to express all the reasons for having concluded a hypothesis. So, the question and answer section, if included in the supplement, may form an excellent part of your work for those who want to go deep.
If the questions and answers are made public, it is possible that the reviewers shall become accountable. Some reviewers suggest very complicated things that you may have missed. Those are the reviews that contribute to your paper, and that particular reviewer should be acknowledged. Some of the reviews may not be acceptable by the author, and for that reason, your article becomes rejected. The Editor may also have no time to look into the intricacies involved. If those reviews become open, then such things can be avoided.
In some cases, the paper shall be rejected outright without a due review process by the Editor of the journal. And, in those cases, the Editor doesn't outline specific technical reasons for rejection. When they specify, it shall be a mere line stating that your article is not commensurate with the objectives of the journal - even when you have used journal selector tool provided on their website to select the right journal. An open review process can avoid all such problems.