To clarify "the press" as it pertains to the First Amendment: When the Constitution was written, there were no major "news media" conglomerates. The "press" referred to therein was the machine used to create flyers, posters and other published materials. "Freedom of the press" encompassed the right of any natural person to print what they wished, even if not favorable to the government. Limiting that right to "bona fide news organizations" is a long-standing corruption of the intent of the Amendment.
However, because that is the way it has been understood and promoted for so long, the idea that individual citizens have those same rights is a hard sell. Also, the party in power in NY, NYC and the USA is working to change the country into something it has never been. Arguments based on history and tradition might not get you very far.