The evident purpose of this proposal is to make it easier to close bad questions quickly. To the extent that it would promote that goal without producing undesirable side effects, I have no objection to it—and I can't imagine that any other EL&U participant would object to it either.
The problem is that EL&U's built-in options for voting to close a question do a very poor job of distinguishing bad questions from good ones. The primary culprit here is the "show research" close reason, which was instituted several years ago to make it easier to close bad questions quickly (sound familiar?) but which in practice makes no distinction between a cruddy question of no interest to anyone but its poster and a question of potentially widespread and enduring interest whose only supposed flaw is its failure to provide background research. Now we have another attempt to make closure easier. If adopted, it will surely increase the number of interesting questions that get kneecapped for a reason unrelated to their quality as questions.
Responses to "show research" closure vary. In some instances, the original poster tries to satisfy the "show research" requirement; in other instances, other site participants attempt to do so (and thereby incur the wrath of certain close voters who consider such efforts to be an exercise in shamelessly presumptuous audacity); in still other instances, reopen voters simply decide that the "show research" close reason shouldn't prevail against a question that they approve of; and in many cases, the question is simply abandoned to its fate. But whatever the outcome, the closure experience is likely to have a discouraging effect on the poster. The natural result of having a fundamentally interesting question closed for a reason unrelated to its inherent quality is to be less inclined to post another question on the site—a point worth considering the next time you wonder why EL&U has so much trouble attracting good questions.
EL&U has an earnest and vocal contingent of site participants whose main interest in the site is in maintaining or raising its standards for acceptable questions and answers. In pursuit of this interest, they seek to disqualify as many bad questions as possible as quickly as possible. But their desire for quick disqualification of bad questions has led them to adopt standards that don't distinguish truly bad questions from good ones. The current proposal accelerates this process without improving the qualitative discernment of the site's approved close vote reasons.
My interest in this site does not primarily involve keeping out the barbarian hordes. Rather, it involves trying to answer good questions. For that reason, I am more concerned about protecting good questions from closure than about closing bad questions quickly.
If (as seems likely) EL&U is poised to make question closure easier, without simultaneously replacing the "show research" close reason with a close reason (such as "too localized") that actually goes to the fundamental badness of the suspect question, I would like to see it also take a significant step to protect good questions from quick closure.
I can think of two simple ways to accomplish this. One would be to link the close voting privilege to demonstrated interest in the area(s) that a question asks about. That is, we could adopt a requirement that, to be entitled to vote to close a question, a site participant must have some baseline score—say, 50 upvotes—on at least one of the tags associated with that question.
A second option would be to give site participants who do have a substantial interest in the area that a question asks about the power to protect it from closure. That is, we could permit site participants who have accumulated some baseline score—say, 100 or 200 or 400 upvotes—on at least one of the tags associated with a closed question the power to reopen the question with a single vote.
Either of these changes would give site participants who have demonstrated an interest in a particular category of EL&U questions a greater ability to weigh in on the merits of posted questions related to that area and to preserve good questions that are at risk of being caught up in the crude dragnet of "show research" closure.