He's not doing any of these things. He's responding to a specific NYT staff editorial.
White agrees with many of you that disproportionate responses to speech happen, are harmful, and are occurring regularly. He cites several instances, from both sides of the American political spectrum. You don't have to come up with an elaborate argument about how White is wrong about how harmful "cancel culture" is; White almost certainly agrees with you (at least in a general sense; maybe not in your particulars).
His point is that you have to discuss something more particular than "the right to speak your mind without fear of shame or shunning". You've never had that right. You can't have it. To be free of shame or shunning is to be free of other people's speech. If you're saying something provocative, you are almost certainly responding in a sense to something someone else said; if you think you have the right to speak without shame or shunning, so does the person you're effectively responding to. At best, you're arguing for what White has in the past mockingly referred to as a "replevin of feels"; at worst, what you're asking for is totally incoherent.
This Substack post would be bigger news if Ken White had, Solomonically, worked out the whole problem of disproportionate responses to speech. He has not, and I think he's probably much too smart to try. He's just critiquing someone else's bad argument. That's all you really have to engage with here; you don't have to let cortisol trick you into believing this is an amassing of the forces of "cancel culture isn't real" that you must mobilize against.