1) She's criticizing the creation of a government-run media organization, not the creation of an org that punishes media organizations for false news. These things have different costs and benefits.
Also, believe it or not, government-funded media already exists. For example, there's Voice of America, Radio Free Europe, the various spokespeople of government agencies like the Department of Agriculture, the Department of Health and Human Services, etc etc.
With that in mind: why should one more new media agency be uniquely offensive?
2) Many of these arguments seem vague and conspiratorial. For example, it asserts that plutocrats really control all of our media. For this, it cites another article by the same author, which talks about Jeff Bezos acquiring Washington Post.
That seems like a pretty big jump to me.
3) Many of these arguments argue things that do not support her point. For example, it claims that the media is pro-establishment. Okay, so what? The establishment has some good qualities.
Imagine the skit from Life of Brian, "What have the Romans ever done for us?" but s/romans/establishment/.