To me, the only plausible shift to more fact-based and balanced coverage happens via subsidies -- the government has to insert itself into the market and put its thumb on the scale. This is unlikely to happen for the same reasons we make every other stupid choice as a citizenry. Also: picture the quality of leaders we vote into Congress and try to imagine them doing anything as high-minded as solving the problems of the news media fellating them half the time, and flogging them the remainder. (Literal extensions of the metaphor juxtaposed with contemporary congressional scandals are left as an exercise for the reader.)
Take $10B of annual spend out of the US budget. Which will never be missed. Fund a public network that only does news. The budget is something like 2-3X FOX News' top line; it's enough to hire real talent and smart leaders. Give the public network one KPI and a new line item: they fund an arm's length fact-checking service or some other form of objective evaluator to score them every day for remaining factual and balanced (and be clear when it's news and when it's opinion). I don't know that you can do 100% facts in the real world -- but can you be balanced, non-sensational, and transparent? The media did a yeoman-like job of fact-checking Trump every day -- apparently we can do this when it sells, so scoring truthfulness isn't impossible.
It seems stupid that we can't take a sub-rounding error of opex out of the budget and do something that would have this kind of positive societal leverage, so maybe I've got it wrong. Even if I don't, we're not smart enough to make something like this reality.