Or it may be the case that the biases of media of different affiliation cancel out so that the overall effect of media is near zero (that is, removing media would not dramatically change the public opinion). It is far from obvious that the media have a common systematic bias which is absent in general population.

There's also the fact that when people think of "biased" media, their minds tend to jump immediately to media that is biased against their own political views

Isn't this exactly what Moldbug thinks? Well, he has no favourite media, but that's the fate of all fringe ideologues and extremists; if you move sufficiently away from the mainstream, you'll have to expect finding few allies.

Also, having no favourite media source is not that rare; I recall that in my country not long ago the boss of the strongest right wing party said that all media are either leftist or German leftist, while the chairman of the strongest left wing party claimed that all media are biased against him.