The problem is that some people believe a fact is one way beyond doubt, and other way believe it is the other way.
Epidemiology: Respirator masks help prevent infectious diseases
Economics: Rent control is always a bad idea
It basically helps reduce the hyperbole/echo chamber effect of such comments/topics. Vice/versa if those topics were "Respirator masks are useless." and "Rent control is always good." then the community notes would tend to go in the opposite direction. It's just a really good idea. For that matter I think a similar algorithm would also work well on general upvote systems at large.
I'd also add that one of the biggest issues with "fact checkers" was not only sometimes questionable checking, but also a selection bias - where the ideological bias becomes rather overt in both directions. Whether that be in deciding to "fact check" the Babylon Bee (in an overt effort to get it deranked), or in choosing not to not fact check statements from the lying politicians that one happens to like.
If the goal were to prevent rents from rising, the mechanism would do so directly, ie. regulate all rent, rather than limiting to continued rentals on certain types of property. Which would by definition prevent rents from rising, presumably along with other undesirable effects.
Anyways, the whole issue with conflating "bad" with objective consequences is the "presumed goal," which is of course totally subjective.
A good candidate for fact checking is something that is well documented objectively verifiable. Politician X said Y on TV the other day.
Well this is definitely false. If you're a politician who can afford a nice place then rent control is a great idea: it gets you elected (look, I made things cheap for you) and keeps you elected (look, I will solve all the problems underpriced rent brings).
I have never seen an accepted fact checking site answer this, which is very strange since it is such an enormous and grave conspiracy theory if it were true. The Mueller report is extensive and quite conclusive in stating that no such evidence of collusion (conspiracy) was not found. Yet fact checkers are happy to check peripheral and far less consequential claims around the case for some reason (e.g., https://www.snopes.com/fact-check/mueller-report-no-obstruct...), but are strangely hesitant to address the elephant in the room.
Or for another example, there were many false or poorly substantiated claims made about covid and vaccines during the pandemic. I saw "reputable" fact checkers address a certain set of those claims about the virus and drugs, but were strangely silent when it came to a different set of claims.
So fact checkers don't even need to provide false content at all, they can be very political and biased simply by carefully choosing exactly what "facts" or claims that they address.
But even straightforward stuff goes unchallenged. Jada Pinkett Smith released a movie trailer claiming Cleopatra was black. When NBC covered the issue, they couldn’t even bring themselves to fact check her. They did a “he said, she said” article asserting that Egypt contested whether Cleopatra was black: https://www.nbcnews.com/news/world/queen-cleopatra-black-egy....
Trump Putin election hacking collusion was always a wild baseless conspiracy theory. Sure there is no absolute proof he did not, and there is various incidental connections and circumstantial evidence you could arrange to fit some crazy narrative. But what it not in dispute is that many people lied and mislead claiming to have "ample evidence" of collusion, when no such thing was ever produced.