The real problem isn't fake news - it's sensationalism everywhere. While Fox et al merely churn out infantile lies for the irredeemably simple-minded, other organizations churn out sensationalist nonsense that totally distorts what actually happened. They do this because, as you note, every "news" organization is in competition with every other for eyeballs. And nothing grabs eyeballs like sensation.

The result is a context free distortion of reality on a massive scale. Everyone reads about the one air crash but no one reads about the 10,000,000 flights that took off, flew, and landed safely. Thus people get a distorted view of the risks of air travel. Covid-19 kills hardly anyone (99.7% of people in even the worst-hit countries have no risk of mortality) but every organization reports endlessly on the edge cases, thus distorting perceptions hugely.

When I was in Paris during the gilets jaunes manifestations, I watched a photojournalist lie down in the road to aim his lens up through the flames of a burning cardboard box less than 1 meter high. The result: an illusion that the Champs Elysees was ablaze.

The problem we face is the universal relentless distortion arising from the competition for eyeballs, not the pathetic lies of the cynical purveyors of far-right propaganda.