Ken White agrees with you that there are disproportionate responses to speech on the Internet and, if you follow him, isn't any more amenable to struggle sessions than you are (see: his years-long advocacy of what Lukianoff is doing at FIRE).
The problem is that the NYT here managed to articulate a different, and stupid, problem: the eroding of our supposed right to speak without shame or shunning. The NYT's arguments are in a line of similar arguments that are not in fact about free speech, but rather the opposite: they purport to defend speech, but only selectively, and in the cases they don't defend, they're an appeal to shut down speech and voluntary association.