No, I'm suggesting that whatever political perspective one has, one has the same right of free speech as everyone else, and that one may, in fact, start one owns "press" at will, without permission or a license from the government. If you want to start a printing press, or a website, or news organization, you are free to do so. You do not need to be a "trained publisher" to publish books, and you do not need to be a "Trained journalist" to be a journalist. You do not need to be trained to be a reporter or commentator either.
Trained journalists who abide by a set of journalistic ethics and have been educated on how to write stories which are sufficiently sourced, backed up, informative, newsworthy and objective will have their work rewarded because more people will take them seriously. However, that does not mean that some jackass Democrat doesn't have the unfettered write to publish his or her views, too.
No no - Harris was referring to Musk as having some sort of "privilege" to operate Twitter/X which she believes need to be fettered - regulated - managed - governed - subject to rules imposed by the government. It should be, in her words, shut down, because he is saying what he wants, not what she wants. That view is pernicious.
X should, of course, not be given protection from defamation claims and fraud claims, etc., if it does not behave as a neutral, open platform. If X becomes the messenger, not the platform for messengers, then it should be responsible for that message. But, as long as Elon Musk acts on his commitment to objective free speech within the law, then X is a platform. That's the same rule that applies to traditional media.