To start with an aside, I think he should practice what he preaches and label Tesla and Space X as government funded companies.
Having gotten that out of the way, I always come back to JP Morgan's quote, "a man always had two reasons for doing a thing: a good reason and the real reason".
My thought is as follows:
Elon's good reason for labeling media as such is that he wants transparency and truth. The real reason is he's said in the past he wants Twitter to be the everything app, which would include being the sole source of journalistic truth. One can only accomplish this by alienating all other media outlets, which he's been very active in doing, and these labels are just part of his censorship attack.
Not defending a lot of the bs that the media publishes, but what I disagree with what he's doing on those grounds.