And besides, if a submission is flagged off the front page by that point I would think the damage is done short of resetting the gravity of the post to allow it to be in the same position on the front that it "should" have been. I'm not even sure if this is something they can do.
Talk to them... they're people.
In any case, someone other than HN (e.g. Algolia) could construct a page/queue of flagged posts for review. It would be used by a subset of the audience for the "new" page.
No permission needed from HN moderators. Users already have the power to vouch for stories, they only need a timely way to review.
Technically and opinion aside, given the weighting function, what is supposed to happen when someone vouches for an eight hour old thirty-five point story? Does it move to page the middle of page two? How is justice done?
To quote Dennis Moore blimey, this redistribution of wealth is trickier than I thought.
I don't think flagging is creating problems in terms of HN's quality. As I indicated, there were lots of reasonable criteria under which to flag the previous post. To me, this post has characteristics that meet those criteria as well.
Where vouching might have a role is a quality story with very few points that is flagged dead based on misunderstanding or malintent. A story that hits the front page has had many eyeballs upon it and if it is killed from there by organic means, that's the way the system is supposed to normally work. Even when I think the story does not deserve it.