I am definitively in favor of that process.  
By the time the 5 "close" votes are here, not enough people are still looking at the question to care to vote for reopening, even if they wanted to *at the time* where closing votes were being (slowly) set.

Of course, it has been proposed "numerous" time on UserVoice already:

- Currently, the "[Add anti-close votes][1]" is ranked 6th, with 179 votes.  
- Before that, "[add "stay open" / "stay close" links][2]", marked as "duplicated", with the comment "numerous duplicates", but without ever mentioning one single similar request.

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Note: since 2014-05-13 ("[When did I get close-vote superpowers?][3]"), users with a gold badge in a tag for a question can immediatly reopen a question closed as duplicate.

This is a (very small) improvement, which doesn't address the initial issue: there is no way to be notified when a question get (finally) closed in order to cast one's own reopen vote.

As I [commented before][4], notification is really broken or non-existent on Stack Exchange sites.  
(That is why I have almost 8000 "favorite" questions, in a desperate attempt to catch some of the events which can change the questions I have answered to)  
... and "close" events aren't detected anyway, even when you "favorite" a question.


  [1]: https://web.archive.org/web/20090527020007/http://stackoverflow.uservoice.com/pages/1722-general/suggestions/143004-add-anti-close-votes
  [2]: http://stackoverflow.uservoice.com/pages/general/suggestions/126069-add-stay-open-stay-close-links
  [3]: https://meta.stackoverflow.com/a/254590/6309
  [4]: https://meta.stackexchange.com/questions/2322/notify-us-when-the-question-has-been-edited-after-posting-an-answer/202139#comment642488_202139