The EFF's proposed fact checking alternative isn't even that good. Let's suppose someone makes a post debunking an American myth like sex trafficking statistics. A small group of people might decide to "correct" that.
Particularly, the more facts that they have to process, the higher the chances there are of things going wrong.
https://en.wikipedia.org/wiki/Scope_creep Scope creep can also be an issue.
I get it. No one wants Zuckerberg to be the arbiter of truth, and demoting content based on the say of a random third party org can be problematic. It would also always be a point of friction and contention, particularly when a fact check is considered to be inaccurate.