The death nail and actual fall of liberalism once you start talking about nationalizing the media. Because there is nothing liberal about state-control and monopoly of how the people get their media and other information. You have to know if you don't already that Free Speech and Freedom of the Press are liberal values and ideas. Its authoritarians either far-left like in Cuba and Venezuela, or the far-right in the Middle East that want to control the media. So they can control what their people hear and not get hurt by that information.
I understand the power of big media especially once it becomes too big and too powerful and starts looking like a monopoly. But that is what anti-trust and anti-monopoly laws are for. Once a company becomes too big as far as how much control they have over the private market the answer is to break them up. The answer is competition, not going from a private monopoly and creating some new state monopoly where now the people in official power can control how we get our information. And even protecting themselves from negative information that can hurt them.