> A lot of times they are closed silently; they accumulate a pile of downvotes, eventually get 5 close votes, and disappear with no indication to the user of what has gone wrong.

This is not correct; there is a clear indication of what has gone wrong: 

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  [![enter image description here][1]][1]

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<s>I think the author of the question gets an extended message with more information, but I am not sure where I can find its exact content (other than asking an off-topic question just for this purpose).</s> EDIT: thanks to Martin Sleziak for pointing out to me in chat that this is [no longer the case](https://meta.stackexchange.com/questions/339700/new-post-notices-are-live-network-wide).

If you believe that this closing message is not helpful enough, please feel free to suggest improvements. What you suggest here is that someone types a duplicate of that message in a comment on every off-topic question, which seems time-consuming and sub-optimal.

Also, keep in mind that new users have to click through another window that warns them that this website is for math research questions:

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  [![enter image description here][2]][2]

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So the blame is at least partly on them for not reading the instructions. (We may also suggest improvements to these instructions.)

  [1]: https://i.sstatic.net/HO290.png
  [2]: https://i.sstatic.net/K3zQP.png