The press has covered the US government since a press existed; that’s why we have the 1st Amendment. As far as who gets to cover it, there’s only limited seating in the Press Room, so more-popular outlets get more seats. You can see a list of the current press corps here. Mother Jones does have a correspondent, as does Rolling Stone, BuzzFeed, Breitbart, and others.
What Jim Acosta had was a “hard pass” – a top-tier pass that gave him access to the White House and the Press Corps offices. They yanked that pass without notice and under false pretenses, barring him from the grounds. This suit isn’t about CNN having specific access rights, it’s about the entire press – who Trump likes to remind us are the ‘enemies of the American people’ – being shown that they can be punished at the President’s whim and that the US Government can make up lies to justify going against the 1st Amendment.
There’s a difference between “we can’t possibly accommodate every publication on Earth in our press pool” and “we will revoke press credentials for any journalist who asks inconvenient questions and lie about our reasons for doing so.”
