Would ELU like to start a trial of only need 3 votes to close/reopen a question?
Update April 30, 2021
Community Managers are working to implement this now.
No, thank you.
To close a question all that is needed are five users with at least 3,000 rep. Just five people out of hundreds or maybe thousands of regular users. Users can cast up to 24 votes per day.
I agree with Andrew Leech, the system is broken not because on January 14, 2020, there are 148 questions in the review queue, which is a TINY drop in the ocean compared to Stack Overflow's +3K, but because the site struggles to find twenty 3k users who feel invested enough to help moderate and keep the site clean.
Maybe the community should invest time in encouraging newcomers to stay, and start upvoting their efforts more often?
There are some EL&U users who only close posts in the review queues, it's very rare that they care enough to edit and keep a question open. I suspect these users will support the initiative wholeheartedly.
I do not.
The Practicalities
- Banner
What if three close voters close a post for three different reasons, e.g. "opinion based", "off-topic": lack of research, and "needs more focus"? Which of the three reasons is shown to the author? Will all three reasons be displayed on the post notice?
Dan Bron, in the comments below, pointed out that the first vote is selected as the reason for closure when there is no clear majority. Here is the relevant excerpt, please note the significant drawback to this feature.
questions closed without a consensus
… And it’s even more problematic because of how we determine the displayed reason: we pick the oldest vote. So if someone picks a bogus reason, that gets discussed a bit and then two other people pick two better reasons… We show the bogus one. @Shog9 (source)
- Reopen Queue
Lest we forget, the author of a question that has been closed by the community can cast a vote to reopen it. Currently when a question enters the review queue it drops out when three users have agreed to keep it open. Will that same number remain or will it be reduced to two?
- Migration
In order to migrate a post to ELL there must be at least 3 votes in favour, by reducing the number of close votes to three you effectively reducing the number of posts that are eligible or suitable for migration.
A little history and an update
As of January 22, 2020, the number of questions that need to be reviewed on Stack Overflow is a staggering 4.8k, little wonder, then, the one-month long experiment promoted by Shog9 to reduce the backlog was greeted with overwhelming consensus and success in August of last year and then finally adopted on December 3, 2019 by Stack Overflow.

Source
The Review Queue on English Language & Usage does not have anything comparable to the above. In the ten days following the OP's proposal, the backlog has been reduced to 126 questions. This site needs more users willing to muck in that's all.