How Can I Improve Another Person's Answer (Beyond the Scope of An Edit)?

Question

I am wondering about what the best course of action would be when one encounters an answer which provides the mechanics of a non-trivial solution, but which is presented in a highly confusing way. In particular, in some cases, I feel capable of filling in the details myself and reworking the presentation of the post, but feel that this would be an inappropriate use of the edit system (since, if I were bringing the post to my own standards with no concern for the author, I would rewrite everything). However, since I'd have no new mathematical ideas to add and could not write a new post without relying on the previous answer's contribution, it wouldn't seem quite right to post a new answer (even if it differs entirely in presentation from the previous one) - especially in cases where the answer is deep enough that, poor presentation or not, it is the important result of the question.

In such cases, I would leave a comment on the answer, suggesting various improvements, but it's doubtful to me that the user would change their post - it could be a big change to execute. I am thinking that, after giving them an opportunity to revise (i.e. waiting a day or two), I'd post a shiny new community-wiki answer, using the same idea, but with a different presentation.

Is my current plan acceptable? Is there a better approach?

(This question previously referred to the first revision of this answer; happily, it has been improved a lot by the author, so the above would not apply to it - I guess waiting was worth it. I have since deleted my comment on the post)

Answer 1

As the commenters said: post your own answer, possibly beginning with "Here is another way to explain the approach taken by X".

A list of answers where additional explanation may be called for can be obtained from Data Explorer: Most hated answers by anonymous feedback. SE collects the voting data from anonymous visitors to the site, even though it does not factor into the visible post score. When you see that the majority of visitors find an answer unhelpful, this may be a sign that something there should be fleshed out in more detail, probably in another answer. (This is not certain; sometimes the answer is fine and the visitors are frustrated because it's not the question they were looking for.)

Answer 2

I think you should post your own answer, but state right at the top something like "User X has presented all the basic elements of a good answer, but his presentation is missing a few key details." And then get to it. If you understand what the answer is saying but you think it's presented poorly, imagine how the OP will probably feel: utterly confused.

Adding a missing symbol or term, correcting an obvious misspelling, putting in missing mark-up, tags, that's what an edit is for, in my opinion. Think of it this way: if you were quoting someone, you might put in brackets:

"Then clearly $x$ can be any [nonzero] number," the professor said.

On here you wouldn't even need the brackets. Anything more than that, and you risk the appearance that you're putting words into someone else's mouth.

The "number ... $x$ can be any[thing]" other than $0$, the professor said.