So to support the goal of waiting a bit to close questions, and under the assumption that once questions end up in the review queue they get closed quickly, I had made this feature request on MSE.
As it turns out, it's already an option! Shog writes:
This already exists - in fact, it's been implemented for somewhere around four years now.
The default delay is... 15 minutes. No review tasks for the Close or Reopen queues will be created until the oldest pending close vote or flag or reopen vote or qualifying edit is at least 15 minutes old. No review tasks for the Late Answer or Low Quality review queues will be created until the post itself is at least 15 minutes old.
The rationale for this delay (for those queues only!) is pretty much what you describe: give folks a chance to provide feedback organically and give the author a chance to fix things before we drag a bunch of other people in.
It's possible to increase this delay, both globally and on a per-site basis... While I see little value in increasing this value across the board, if folks on a given site believe their topic or audience warrants a longer delay, then this is trivial to increase - just propose the change on the proper meta site(s) and let the people who'll be affected by it discuss the pros and cons of various values. If there's consensus, I'll make the change.
This means, if we can reach a consensus on it, we can have the amount of time between the first close vote and its appearance in the review queue delayed.
The feature exists already exactly for the reasons I proposed: To give people a chance to clear up unclear questions and such before the question is put on hold, while at the same time letting the community delay close votes without the need for e.g. bookmarking review lists offline or periodically performing mass cleanups. To me this seems like exactly what we want here.
However: There is a caveat here: This delay also applies to the reopen queue, both for reopen votes and for edited questions. This is the flip side of this coin. Striking a balance may require diligence in other areas, which is probably a conversation for another post. Let's see where this discussion leads us, though.
So then, what do you guys think about a longer delay? Perhaps a day or so? The purpose of this discussion is to determine if we want a different delay and, if so, how long. We could probably talk about how we can effectively deal with a longer reopen delay here too, but there's a lot of approaches to that and it may be difficult to discuss in comments.