This is a really excellent analysis. The question isn’t whether Twitter in general is subject to the first amendment—it isn’t. It’s whether government officials, by creating a Twitter account, have in effect created a public forum. Having done so, they can’t restrict speech on it. This isn’t a far out argument, though it might seem like one. Public forum doctrine is well established.
To use a meat-space analogy. Say the government set up booths in a mall for public officials to make speeches. Could the government then kick out people who bring in pro-abortion signs to such a speech? Probably not. While there is generally no free speech right in a private venue like a mall, where the government creates in effect a public forum on private property, it has to abide by the First Amendment.
Were the law otherwise, government officials could insulate themselves from criticism simply by making speeches in hotel ballrooms and the like. That is, in effect, what Trump is trying to do with his Twitter feed.
To use a meat-space analogy. Say the government set up booths in a mall for public officials to make speeches. Could the government then kick out people who bring in pro-abortion signs to such a speech? Probably not. While there is generally no free speech right in a private venue like a mall, where the government creates in effect a public forum on private property, it has to abide by the First Amendment.
Were the law otherwise, government officials could insulate themselves from criticism simply by making speeches in hotel ballrooms and the like. That is, in effect, what Trump is trying to do with his Twitter feed.