No. I would neither discourage nor encourage its use.
It requires readers to read a post, assemble some understanding/mental model of the ideas presented, then discard those in favor of later words representing changes to the previous ideas. You may think I'm overreacting, but look at edit 4 (!) on this post: it completely changes the constraints on the question.
You are making an assumption that all edits are placed at the end of a question, which is simply not the case. Edits at the end of a question do make sense in the case of information that was never in the previous version of the question and are thus not a problem. One (or a percentage) poorly formatted question does not make a certain syntax universally bad.
It makes the posts themself look less expertly-done. The hallmark of all Stackexhange sites is the presence of expert users and expert content. Having "Edit:... Edit 2:... Edit 3:..." undercuts that. (This is not hyperbole.) Instead of coming to a site and finding interesting and well-written Q&A, we come to a site and find interesting (to some)/frustrating (to others) streams of consciousness.
This is opinion. A valid opinion, but still an opinion. A lot of what we do here requires a poster's thoughts to evolve before a final question comes out of it...I do not mind that on the page personally. That is my (also valid) opinion.
It's redundant. We have revision histories on all posts. They're really good revision histories. They're not hidden, as clicking on "edited XX ago" is available to all.
That's great but I can't recall looking at it on more that one or two occasions, and it was mainly because I answered a question, an edit was made and I wasn't sure where it was...which again, is why I do not mind someone pointing their edits out in the question/answer...it's easier.
I prefer to lean toward the benefit of askers and answerers. These are the people truly engaged in the question. People passively reading a question are far less of a concern to me than active participants...after all those passive readers have nothing to read if the participants don't write anything down.
I am not advocating that we encourage this format, I am simply saying leave well enough alone and leave it to the poster.
If you believe that a format change would make the question better, feel free to edit the post. If the poster doesn't like it they can always roll it back.
Worldbuilding is not an exact science...asking a question here is much more complicated than asking a question about coding or chemistry, it should not surprise anyone that edits are common...therefore, while the question is being actively worked, I find the syntax valuable. If we want to mention that once an answer has been accepted it is good form to clean things up that is fine with me.