That would be counterproductive. The reporter would get abuse from random people, the article would definitely get published with the blogger's name, with the twist of "blogger tries to suppress publication of article by leveraging an online mob."
I would like to know who the journalist is. Not so they can be threatened or put in danger. But so their reputation can take a hit. Part of the reason people do these things is because they can get away with it without any consequences.
The lead editors are responsible for maintaining ethical standards, and they represent the NYT. Adjust your impression of the NYT reputation based on this story. Also see the other comment on this article about Naomi Wu being doxxed, where the risk is deadly living under a tyrannical regime: the NYT hired the journalist responsible, who doesn't believe any mistake was made there.
It's just assumed in your comment that this should only be about the media outlet, and that we should ignore the journalist involved.
The problem with people trying to shut down others primarily comes from individuals. Often that's individuals on social media. In this case it's a journalist. These individuals can destroy other people's lives, yet they essentially face zero consequences for doing so.
And each time they succeed, like in this case, they embolden others to do it.
For twitter, you have a point. For something being paid for and published by an organization, this is driven by the organizational culture which pays them to do so.
So Scott the psychiatrist's reputation can take a hit? If Scott Alexander writes shitty stuff, Scott Alexander's name will take a hit. And there's nothing wrong with that, because his future work will also be published under that name. But what's the rationale for nuking Scott the psychiatrist? (who will also be nuked even if his patients see nothing wrong with his blog. Patient-psychiatrist interactions are supposed to be tightly controlled)
Colleagues, sure. Patients, NO. Especially since this will harm even potential patients who would have had no problem with Scott. The problem isn't that patients will read SSC, decide that Scott isn't cool, and Scott loses business. It's that patients will read SSC, learn too much about how and what Scott thinks, and this will hinder Scott's ability to help these patients regardless of what said thoughts are. For instance, if Scott talks about hating PE class in high school (he very well might have, I don't know), that could stop patients from opening up to him about their passion which happens to be sports or something.
But, you say, surely that's not a problem for well-adjusted people! Guess what the hell a psychiatrist does.
There is no need to do that. As long as the reporter remains unnamed, for now, they can decide to either not publish the article, or not publish the name, and they will be able to go along with there life, without getting the negative backlash.
If they do dox the person, though, their name will be on the article, and you'll be able to find it.
Since it seems that the reporter might have been named after all, did anyone take a quick look at their previous work to check whether they have a history of publishing problematic or misleading 'hit pieces'? It might be useful to figure out if concern really is warranted here.
Part of the reason people do things like what the journalist did is because they can do so without facing any consequences. There should be disincentives for that kind of behavior. I'm not talking about them being threatened or put at risk. I'm talking about there being consequences for their reputation.