If Bitcoin was published as an economic newspaper, like the Financial Times, its blockchain would be constitutionally protected. So, what's the problem?
The First Amendment to the US Constitution prevents the government from making laws abridging the freedom of the press. It protects publication of information and applies to a wide variety of media, including newspapers, books, movies, plays, video games, and more. Freedom of the press was described in Branzburg v. Hayes as 'a fundamental personal right', not confined to newspapers and periodicals.
The First Amendment also guarantees freedom of speech. But why doesn't 'press' fall under the freedom of speech clause? Freedom of the press protects the right to use the press as a technology, from the printing press to modern implementations such as blogs. Freedom of speech focuses on the spoken word, while freedom of the press focuses on information that is published using technology.
Bitcoin and related technologies allow nodes (authors) to publish new blocks (news) to a blockchain (newspaper). Blockchain technologies can be considered a publishing platform because they allow information — including text and images — to be transmitted.
Chief Justice Charles Evans Hughes (11th Chief Justice of the United States) defined the press as "every sort of publication which affords a vehicle of information and opinion". He didn't know about blogs at the time, yet blogs are protected under the First Amendment. Freedom of the press not only means the freedom to publish information, but freedom for citizens to be able to read it.
Restricting the use of cryptocurrency, it can be argued, is a violation of First Amendment rights. If a business enterprise wanted to publish and distribute their accounting ledger as a periodical, for whatever reason, they'd have the constitutional right to. If you wanted to publish and distribute your own ledger and call it Bitcoin — or one that force-multiplies fiat — well, now, that's a problem.