This. This is the problem.
The value of free speech goes beyond what is Constitutionally guaranteed. It goes far beyond that. If you stick to what the Constitution guarantees and no more, you can end up in a rigidly thought-controlled dystopia. I have higher standards. You should too.
First, let's clear up cancel culture (when directed against someone for what they said). The idea behind cancel culture is that if you say the wrong things, you will suffer negative consequences, sometimes including tangible physical consequences (job loss, harassment, etc.). Faced with these consequences, one might expect many to self-censor; those who don't will be punished. Either way, consequences are meted out on the basis of disfavored speech.
Now, let's suppose we enact a law to do this: after deliberation, the legislature makes it illegal, punishable by severe fine, to engage in some type of speech; and if you do or are thought to engage in such speech, you'll be tried via the judicial system and, if convicted, be sentenced and suffer the consequences. Pretty bad, right? Unconstitutional. Definitely.
Okay, then. Let's instead have the "law" created at a whim, and sentencing occur by mob action. Better?
Maybe we should try handling murder cases this way--we'll just have people decide if someone was killed and who the killer was, and go out and enact justice. Good idea?
Constitutional guarantees provide a backstop against dangerous encroachment by government into authoritarianism. They are insufficient to ensure a tolerant, discourse-affirming society.
This quote puts it well: Most important, freedom of speech is the bedrock of democratic self-government. If people feel free to express their views in their communities, the democratic process can respond to and resolve competing ideas.
Not bad for a "stupid op ed about free speech" (which you cited twice--citing the same piece twice doesn't mean you have twice the evidence!).
They nailed it. You missed. As you see from the comments, you probably hit your thumb, too. Not all the commenters are buying your viewpoint here.
The government, it is true, does not enforce a lack of criticism, mocking, shaming, scorning, and teasing. But we, as responsible members of society, should wield such things in a way fully consistent with people feeling free to express unpopular ideas in good faith, or what is plausibly good faith.
The irony in your argument is immense: "the aim of such an argument is to demonize dissent, to kneecap robust debate before it even starts". So you say. Except you are the one advocating for the demonization of dissent, because you are the one implicitly endorsing being "criticized, mocked, shamed, denounced, dragged to filth"...in other words, being demonized.
Furthermore, I note your repeated refusal to address the insidiously destructive effects of blacklisting on public discourse and people's lives--blacklisting which was entirely okay according to your arguments. This is particularly telling, because it dramatically undermines your entire thesis--so naturally it's awkward to have to actually address the issue via argument.
But, in the marketplace of ideas, such as it still exists, you cannot so easily sneak away from unpleasant evidence, because people will call you on it.
In summary,
(1) Constitutionality is a red herring. This is about structuring civil discourse, not the bounds of legality.
(2) You hypocritically charge the NYT of demonization when you advocate for it yourself and they do not (in what you cited), and
(3) When the very apt historical parallel of blacklisting is brought up, you ignore it.
There aren't many situations where the paradox of tolerance is a real paradox, but I think you may have hit it here: your embrace of speech-intolerant speech threatens tolerance of speech due to the potential effectiveness of speech-intolerant speech.
I advise you to either rethink your position, or how you express it, because this article just doesn't make its case.