I will share some of my thoughts.
The main reason you run into these disagreements is, AFAICT, the following:
Various users on our site hold wildly differing ideals of what they want the site to be like. This will then reflect on what kind of material they upvote, downvote, vote to close, vote to keep,...
As a metaprinciple I think that for the site to function as smoothly as possible, we need to form policies/practices that accomodate as many ideals as possible, allowing them to coexist peacefully.
For the most part the ideals of different users are compatible. We also have many tools we can use to re-evaluate and discuss the small fraction of cases where the ideals pull into opposite directions (c/r/u/d queues, meta,...). Also, the privileged users can take action and repair the doubtful questions. If I got it right this feature-request is asking for yet another tool to be added to the existing ones. The two motivations for the feature-request seem to be (correct me if I'm wrong)
- to reopen a wrongly closed question quickly, and
- to be able to explain to the close voters why somebody disagrees with their vote.
I am not comfortable with either of those motivations. For the purposes of getting a question reopened (and for the purposes of preventing similar clashes in the future) the requested feature actually seems counterproductive to me. Let me elaborate a little.
- The users who voted to put the question on hold already gave their opinion. With a view of garnering support for the opposite view it is surely more efficient to ask for opinions of other voters. To that end using the reopening queue and/or the dedicated c/r/u/d meta thread is obviously a better choice because then you don't need to fight against the first impression those voters had formed.
- Explanations force-fed (via a comment) to a user who already voted is similarly ineffective. This is particularly so, if their different voting decision was based on a different ideal about the site as opposed to a simple misunderstanding the question. In that case sending them comments will soon amount to harassing them, and is thus counterproductive. The ideals various users have lie deeper in their minds. I like to think our core users keep an open mind, but any changes in the core ideals only come gradually (if at all). If the difference in views comes from a small technical misunderstanding then, sure, pointing that out would work, but it is still at least as efficient to ask for opinions of users other than those who already voted.
For these reasons I oppose this feature request. A further reason is that the feature could easily be abused to harass other users. I don't think it necessarily would be abused, but the potential is there.
The above was a bit abstract, and I may have failed to communicate my thinking clearly. Therefore I also discuss the thread the OP used as an example.
To any mathematically trained brain it is clear that the question about a graph model of Wikipedia is woefully underspecified. It is not really my cup of coffee, so I would only stop to think about it under special circumstances. Imagine a scenario where I'm on a long flight, striking a conversation with the passenger next to me, and, upon learning that I'm a mathematician, they would fire this question. It would not be polite to dismiss it outright, so I would reply with something like:
- Hmm... The average could be infinite. After all, the Wikipedia could consist of hundreds of thousands of clusters of 21 articles, all linked to each other, but no connections whatsoever between the clusters. If the fellow passenger can follow that, the special nature of the counterexample will likely frustrate them. But, you see, that's how a math brain works...
- ... OTOH, if we assume a tree-like structure of the graph, then each jump will multiply the number of nodes within reach by a factor of nineteen. Let's see, the average comes out as...
- ... But, that is also an unlikely structure of the graph. A better estimate might be gotten by assuming that the links are random, when in the next layer we can assume that the fraction of links to already covered nodes is...
It would still be clear to me that the last model of "uncorrelated" linkages is not realistic. Surely most of the links go to closely related topics, and relatively few jump "further out". My point is that I assume most of the voters to also have reached this point in under two minutes - we have very many users in or out of grad school, and they wouldn't break a sweat here. Of course, to an expert on the statistical properties of random graphs there would be more nuances available, may be even a realistic model leading to a realistic answer. Michael, if you have such expertise and can answer the question without reproducing scores of pages from a relevant textbook, do explain that in the reopening request meta thread!
So if this much is clear to all and sundry, why the votes to close? I can only speculate (I would not have voted that way, see below). I tend to think that we have a faction of users who believe that the questions should have definite answers. Their ideal of acceptable questions matches closely with what could be used as exam questions in an appropriate course. According to such an ideal this question is rubbish. Because the clash is (probably) with their different "core ideal", pestering the close voters with comments sounds like a bad idea here. It is not unlike trying to get a life long White Sox fan to switch their allegiance to Cubs (they won the world series, you know!). It is not going to work easily, and only serves to annoy the other person.
But, my sentiment is with you on this one. I would personally like to be more accomodating for questions like this from reasonably educated laymen (obviously that is the case here). See item #1 in an old answer of mine for some elaboration.
However, it looks like many disprove of such questions.
Also, I confess to being a bit too proud of my ability to make sense of a question others rejected. I guess I'm not alone here. I have been relatively successful in making such questions palatable to others. That takes a lot of work per question, but when a question tickles my vanity bone... Actually the other users are quite accomodating here. When I work hard improving a question, and, apologetically, request it to be reopened in spite of its shortcomings - all that to be able to post an answer earning 25 points rep (all from the asker) - the others will let me have my fun. The same general approach might work for anyone else.
Don't try to force your ideal down other people's throats. Play along instead, and they will let you play, too.
We are well into TL;DR; territory already, so I leave the details of my success stories (as well as a few more shameful ones) for another time.