> ... shows me how factual each source is and which way they lean politically.

Fact-checkers and whatever you call people that gauge political biases aren't impartial sources of information. Someone pays their bills and those people typically have agendas besides delivering objective truth.

I'm not suggesting that paying monthly fees or paywalls are a solution to the problem either.

The real solution is to stop reading the news IMO. Let these companies go out of business and get replaced by something better. If one must read the news, just use an aggregator and archive.is for bypassing paywalls.