Jules Thank you for your feedback. Since only admins have access to settings, it also makes sense to only let admins make changes to quick replies. If you would give access to settings to everyone, it could cause irreversible damage if someone makes unauthorized changes, so it's not something you would want. Also for the sake of keeping your quick replies organized, it's not preferable for everyone to be able to create quick replies. What you could do is create a team chat where agents can submit quick replies for admin review.
User based quick replies, so that they would not be visible to anyone else but the creator, could work. We will keep this in mind for future iterations of related features.