I have a flag on my platform that flags users who reported things I agreed with the removal of, as "trusted" and their reports are given more weight in the algorithm next time. Sort of the inverse of what you propose where everyone is somewhat untrusted by default. (But not entirely untrusted.)
There is apparently an entire branch of research called Reviewer Reliability. Someone on HN pointed that out to me a couple of years back, when we were discussing the problem with fake/bought/manipulated/blackhat product reviews.
In a hilarious twist of fate, searching for that term brings up papers on either medical research or peer-review reliability problems in general[0]. You try to find data on a potentially abstract, complex societal issue, and come up with what can only be described as attention grabbing HN-catnip.
It's possible to email the mods vouching for stories (or comments). I do this fairly frequently. Not (yet) in this case, though there was a politically-tinged story earlier this week that I alerted mods on.
What's particularly insidious is that killed stories both don't show up in Algolia search results (this is somewhat understandable, but in the case of political flagging, problematic), and even where favourited (something I also do with some regularity), may not be visible to non-logged-in users and IIRC actually disappear from the index in time.
My proposed approach is a little more automated. The mods don't have to find and remove flagging rights individually, they just unflag a post and instantly all the users who had flagged it lose some credibility for future flags.
EDIT: The "flagging trustworthiness" could even help mods to find posts which might need to be unflagged quicker based on the average trustworthiness of the flags.
But unfortunately that could lead to a chilling effect on flagging deserving content. I like having dang and other moderators involved as the final say to reverse a decision if it's necessary. I am pretty conservative with my own flagging and vouching (I've vouched precisely once and it was a comment I strongly disagreed with but was clearly made in good faith and added to the discussion) and I believe that other folks are as well. Since the system mostly works and since social media upvoting algorithms are so insanely complicated to balance well I think it's fair to avoid rocking the boat.
i would like an option in the settings to disable/enable my ability to flag content. On mobile, I have accidentally flagged things and recall it being challenging to hit the button to unflag.