Just, as an example, not casting any aspersions...
If your community is made up of people who either lean right, politically, or are far right, politically, then your Community Notes feature could still "work" in that there would be strong disagreements between whether Trump is a literal God King and whether Biden's policies are actually doing what fiscal conservatives want. You would get a spectrum of beliefs and you could get "corrections" that bring you CLOSER to a truth, maybe (splitting the difference between "empirical" and "some shit you made up" brings you further from truth, but let's press on), but you still won't get any real "fact"-checking. You'll just get a big fat "actually, you're an outcast in this society for this view" sticker on your thoughts.
In the name of fairness, you can replace the above thought experiment constituents with leftists and the result is the same. Notes that urge users toward or further from "defunding all police", or "abolishing the second amendment", etc.
And then, of course, the reality is in the middle-ish. I will make a firm contention, here, that Twitter IS more politically right than left and it shows in the platform's third-party observed metrics, as well as the content of the Community Notes. But I also think that the political classes of twitter are a much smaller portion than, say, the J/KPop stans, the Swifties, or the product people (individual creators selling things, like webcomic artists rather than, say, Tommy Chong's weed gummies). So there's a strong raft of leftist politics, it's just that they aren't the ones who engage in Community Notes. Children, Fans, and the chronically overencumbered do not tend - at least in the metrics I've seen (and screamed as "duh" by my brain) - to engage in policing misinformation. So you end up with a Community Notes that settles on 'rightness' via a right-leaning community consensus, rather than any actual facts. Which is... not the intended effect. Now, granted, it's less biased than other systems I've seen, but that doesn't excuse the amount of bias it ends up displaying, practically.
So the issue is that without the general public, or at least representation for all of its demographics in proportion, you don't get closer to truth, you just get closer to community consensus. It's a utility that works BEST at consolidating viewpoints into mass-appreciated ones, and has a limited tendency toward truth as a side-effect.
So why is the general public not proportionally represented on Twitter? Like I said: Musk. Whether you appreciate it or hate it, his personality is polarizing and a lot of people just won't engage with it. They left Twitter and it surged right. Again, not to it's complete subsumation as a lot of media would "have you believe" (more likely, media leaves out unnecessary details and people run with that to make it feel like it was intentionally dishonest), but it's observably more right, politically. Source: all third party reports, and spending every single day on twitter with 16 separate accounts specifically for monitoring trending content.
So, unfortunately, he built a really cool little thing that does actually work! But it worked better for old twitter, and doesn't particularly work well for getting "facts", now. All types of people have to engage and you only get all types of engagement if you aren't so hyper-focused on your own dumb bullshit.
Instead what he made was the best little shit-stirrer for his echo-chamber. Great, if that's what he was after. But hilarious if he was actually trying to get something approaching "truth".