I guess it was I that enticed this question, by a comment on your earlier question, so maybe let me clarify what I meant.
Here is what I do, when I review an edit: I focus on the edit, with highlighted differences. Often times the situation is clear by doing this, but sometimes there is a doubt on "what is going on in an edit;" this is exacerbated by the fact that the preview is not perfect/complete. But sometimes it is also not completely clear what the intent of an edit is, or why it is justified.
In such case I look at the edit-summary, sometimes this helps. Sometimes not and I might go to the actual post for further information. But sometimes I might just overlook something.
Here are some things that can happen, and I believe to have noticed them happening.
There are minor edits to the post and an important retag. This can easily get a reject if the reviewers are focused on the edits and neglect the retag. If the edit summary says: "retag this to that and minor formatting changes" this might help. It makes clear the point is the retag.
There is one important character to be changed to fix a formula. To get past the character limit one does some minor things in addition. This also can get easily rejected. Especially as preview is not complete. If the summary says "fixed formula, and a few typos corrected" it can help to draw attention to the formula.
Some information from comments by OP is included. But, how will the reviewer know it is from comments by OP and not an arbitrary third-party addition? The review summary could explain it.
A minor edit is done to an old post shortly after the thread got reactivated for some reason. Some users do not like old posts being reactivated for little touch ups. But, if in fact it already was activated before that point is moot. The review summary could explain this. "Minor touch ups, while thread is on front-page."
Generally, a detailed review summary can help to convey what the editor wants to achieve and/or document that they know what they are doing.
I do not think that a suggested edit should ever be rejected only because it has a poor edit summary. What I believe can and does happen though is that an edit gets rejected because it was not completely understood and this misunderstanding came about because it had a poor edit summary.