Some of our billionaires?
So, two things. The Fairness Doctrine was a rule issued by the FCC in 1949 that stated that broadcasters had to present controversial topics in the public interest. They also had to present those issues in a fair and equitable way. So basically they had to provide information about say, civil rights, and do so in a way that was not sensational or leaned to one particular side or another.
That is the Fairness Doctrine in a nutshell. It was also limited to broadcasting when there was limited band with. There were 3 major broadcasters in the 50's and they controlled television. Radio stations were also fairly limited. Once cable came onto the scene and FM expanded the dial for radio, the Fairness Doctrine wasn't super influential.
What you seem to be talking about is the 1996 Telecommunications Act, which deregulated the media markets allowing buyers to pluck up media outlets without regards to anti-monopoly laws. That is the law that allowed right wing outfits to saturate the markets.
To the title of my response... To which billionaire do you refer? We know some of the players on the right, The Koch's, The Mercers, Adelson, and the Corporations. Who are the liberal Billionaires who would finance "left radio and TV"? George Soros? Bloomberg? (he's a center right guy), Buffet? Steyer? While they tend to support more liberal or moderate policies and are against the type of fascism being pushed by the Republicans now, they are not going to fund, to their financial demise, media that works against their interests.
Right wing billionaires pour money into right wing media even though it is a money loser because they want to create voters who will support policy that pays them MORE than they invest. The Mercers invest 100 million into radio, but get tax cuts of 3 and 4 billion dollars. Buffet is going to put money in to radio that promotes raising his taxes another 100 million dollars? Maybe, but his billions won't last too long with that strategy.