There was one other notable exception to free speech that undermines your point: obscenity is not, or has not been, considered speech under the terms of the free speech amendment. So, at least historically, there is some precedent for considering that some forms of human expression can be censored on their own merits.
I should note that I am anti-censorship and consider such laws absurd, but my point is that we can't rely on readings of the constitution to self-evidently protect us from such things.
Many poor precedents are grounded in strong emotional reactions at odds with basic principles, and in my opinion obscenity cases are a good example of that. Still, the classification as obscenity is more about the form of the speech than its content. In fact the more content there is, in the form of either expression or artistic value, and the more the form contributes to accurately conveying the content of the speech, the more likely it is that the speech is considered protected, even if the form would otherwise be considered obscene. I'd rather the courts didn't get involved in trying to decide whether a controversial turn of phrase has enough merit to warrant protection, but in any case I don't think you can extend the principles underlying prohibition of obscenity to exercising control over which information can be conveyed.
obscenity is not, or has not been, considered speech under the terms of the free speech amendment.
What part of "shall make no law" isn't clear? It's true that obscenity is an exception to 1A, but that's something that some people made up after the fact, in direct contravention to the framers' stated intention.
The founders weren't short on ink. If they had wanted to equivocate, they were certainly free to do so. The fun really starts when some people decide that their (least) favorite amendments are subject to less (more) interpretation than others.
I should note that I am anti-censorship and consider such laws absurd, but my point is that we can't rely on readings of the constitution to self-evidently protect us from such things.