I dont think being dismissive of pete is a good enough answer, so i wll spell it out a bit as I see it.

Leave the current administration aside for the moment and think of all politicians everywhere. How often do they admit they have done something wrong or step down over an offence before it is the public eye? Even when they apologise in Parliament or elsewhere you will see their and their collegues statements are much more "Sorry for being found out" than "sorry for doing wrong." It would be better if politicians stepped down when they did wrong, but they don't. For that reason mechanisms to hold them to account are vital. And for all its faults, that is one of the main roles of the media.

By restricting the media to only those "on your side" you stop this happening and so free the politicians from any form of critical assessment. And this is one part of the first amendment: it forbids any law infringing the freedom of the press. Unfortunately the people who framed the amendments were lawyers so it did not occur to them that there are plenty of other ways of infringing the freedom of the press without creating laws. Nevertheless it is clear the intention was to ensure the goverment did not interfere with a free press.

The President has also made noises saying he wants all sources to be identified. Cast your mind back (if needs be) to when you were say 30. Imagine you have strong grounds to believe your boss is committing a crime - fraud or embezzlement perhaps. You do not have photographic evidence. Are you prepared to go public and risk not only your job but also all your future career? A few are, but most of us are not that brave. An anonomous means of alerting people to this is essential, or the crime continues undiscovered. The press have always been one of these options. Cutting this will, as Trump said, cause a lot of the stories to dry up. But it will not stop the crime and it will allow more.

Of course the media is far from perfect and often frankly despicable: no one says otherwise. It would be great if it did more investigative journalism and less froth. But even with all its faults it performs a role vital to an effective democracy.