This also isn't about stories posted by news organizations on Facebook. It's about people posting links to news stories on their own pages.
The news media needs to put up strong paywalls and give up on full subscriptions. No one wants to pay $100 per news source to access hundreds of articles they don't want to read. They need to let people pay per article. Paying one article at a time is too expensive due to transaction fees. They need to offer something like 40 articles for $20 and request another payment when the 40 articles run out.
The news media needs social media to spread their article links around. Charging social media per click will result in their article links being reduced or blocked because of the cost. News media with lower cost links will be promoted.