This question attracted a comment that seems relevant and helpful. Unfortunately, the user who tried to leave this comment is new and has a reputation of 1. The user could not leave comments, so elected to propose an edit containing their remark. Since new users can apparently propose edits, which are applied after moderation, shouldn't it also be possible for new users to propose comments, which will appear only after moderation?
7$\begingroup$ Another workaround is for a user to post an answer, which a moderator can turn into a comment. $\endgroup$– Gerry MyersonDec 2, 2014 at 4:46
The question in the title is quite different from the one in the body.
What is to be done about replies left as edits?
Reject the edit, and if you think the information is relevant post a comment containing it, like "user12345 tried to leave the following information via an edit:..."
Shouldn't it also be possible for new users to propose comments, which will appear only after moderation?
The point of view of SE is that comments are not that relevant and should rather be minimized. Thus, it is unlikely they will implement this. Indeed the proposal came up see Allow anyone to comment but hide low-rep users' comments until reviewed for various discussion.
Furthermore, as Gerry Myerson mentions there is the option of passing through an answer that is then converted. This type of behavior is approved by moderators in case of relevant comments.