I’m afraid the basis on which your argument is made is shaky. The First Amendment was not rooted in concerns about the government controlling speech in general. It was rooted in concerns about criminal liability for contra-government speech as reflected in the seditious libel laws in England that had been in place since the 1500s. Like, you could go to jail for criticizing the government.

If you study our jurisprudence you’ll find that no free speech cases were decided by the Supreme Court despite plenty of common law surrounding speech such as civil libel, commercial regulations, etc. for nearly 150 years (!) until the early 1900s. Debs v U.S. (1919) was the first case and it was about - surprise, surprise - an anti-war speech.