It's nonsense. Constitutional governments with checks and balances can and do hold up to criticisms against them, even speech advocating against free speech. The paradox doesn't exist because the premise of the paradox, that tolerance of the intolerant inevitably results in the victory of the intolerant, isn't true.
Which even still isn't a hard rule, there's a few well known examples of remaining tolerant (not trying to prevent your opponents from speaking) in the face of intolerance (your opponents do try to prevent you from speaking) and succeeding rather well.
Yes, that's the point. The popular way of using it to justify starting violence yourself is not an accurate reading.
The 20th century alone is not short on case studies. Again and again the empirical outcome of tolerating bad faith weaponized speech is the sharp reduction in the diversity of ideas and perspectives actually present in speech, by violently silencing or eliminating those who hold other perspectives.
So the problem isn't 'tolerating bad faith weaponized speech' but rather tolerating 'violently silencing or eliminating those who hold other perspectives.'
The second does not follow on from the first.
Also, what is (and who defines) 'weaponized speech'?
Likewise, who defines 'bad faith'?
The proof is in the pudding, the American system of political tolerance has an excellent track record and leads to better outcomes in the long run.
The paradox doesn't apply to actors operating in good faith who simply disagree, but those whose intolerance extends to authoritarianism and violence in oppressing the free speech of their opponents, such as the Nazi regime that insipired it, and its truth seems self-evident. You'll have to explain to me how greater tolerance of the Nazis would have resulted in a better outcome for anyone (besides the Nazis) than intolerance of them in order to disprove the premise.
The supposed paradox of intolerance says that silencing people who would silence you is the only way to prevent yourself from being silenced, but this is demonstrably not true.
They have eliminated 100% of conservative voices from the platform, as a result it's become a haven for leftist extremists who now openly and repeatedly advocate for moving 'beyond electoralism,' the meaning of which is well understood.
This is uninformed dogma, and reads as if you've lived under a rock the last few years. But to speak to your broader point about the paradox of tolerance, we don't owe a platform to speech that advocates for killing others, which is by definition also an attack on the free speech of those others.