>Why would the alternative be carte-blanche over all forms of property?
Because the rights of property, free speech and association that apply to social media platforms apply everywhere, so altering those rights for social media platforms also alters them everywhere.
>The government already forces telephone companies not to discriminate based on speech. Broadcasters must follow restrictions and allow government messages to be played under certain circumstances.
Social media platforms are not common carriers. They don't have monopoly over free speech or the dissemination of information, nor has any platform ever claimed to act neutrally. The entire business model of social media is curation and algorithmic recommendation of content - the exact opposite of what a common carrier does.
Also, broadcasters are regulated because broadcast spectrum space is a limited resource. Cable broadcasters, for instance, aren't subject to the same regulations.
>What would the harm be in making a law along the lines of "A digital service used primarily for communication with over twenty million members must allow sitting members of congress, the supreme court, the president, and members of the cabinet to disseminate any communication they so desire during their tenure."
The harm is that the First Amendment prevents the government from abridging the people's freedom of speech, and a fundamental part of freedom of speech is freedom from compelled speech. Forcing all social media platforms which meet some arbitrary (and arbitrarily changeable) limit on membership to carry speech by the government is compelled speech, and an abridgement on freedom of speech, and thus voids, or at least weakens, the First Amendment. Which is a bad thing.
Governments already have their own media infrastructure. Members of Congress, the Supreme Court, and the President of the US have Twitter accounts (remember, what was banned was Trump's personal account, @POTUS is still perfectly fine.) The solution here is for the government to either comply with the rules set by social media platforms like everyone else, or else create their own platform.