Since at least the early 2000s, and certainly throughout the Bush and Obama administrations, the media has felt perfectly free to basically ignore any Presidential press conference they didn't think was interesting. You were doing good if the media passed on a few soundbites or put a story about it (in their words, with their framing) on the front page.
Twitter, for better or worse, gives you direct access to normal people. I'm no fan of Musk, but I'm inclined to believe that if our financial (and in the example, political) system is so fragile that tweets can blow it all to hell, we have a serious problem and system collapse is inevitable.