Your question is excellent and gets to the heart of the matter.
How could Facebook, in a neutral way, cull crap and promote quality?
I wish I had robust answers. All I have at the moment is opinions.
• Algorithmic methods can't deliver near term solutions. Algorithms embody the biases of their human coders. I doubt we currently know how to algorithmically evaluate inputs for quality in the Facebook or "fake news" context. We need more time and effort to learn how to do this.
• Promoting quality currently requires humans, who are expensive. If Facebook really prioritizes feed quality, we'll see serious hiring. If we don't, then evidence of commitment is lacking.
• I believe (no proof to offer, mainly intuition) quality can eventually be algorithmically determined, but it's a hard problem. It will take years, lots of smart people and $ to figure out how to make it work at scale.
• I don't think Facebook's announced path, which is to solicit those who are arguably more susceptible to "fake news" to be arbitrators of quality, will succeed.
Facebook, like others, is caught between maximizing 90 day quarterly profits and becoming a persistent human resource. I don't envy Zuckerberg at all. I hope he can do the right thing.
We'll see.