What do you mean? Alexander said himself that he was doing this as a protest and publicity stunt, and he seems to have taken no actions beyond that publicity stunt to make the content less available (e.g., he hasn't (yet) requested deletion from the Internet Archive). His words and actions seem entirely consistent to me, so I'm not sure why you doubt him.
1. I believe the New Yorker reporter disingenuously made a statement that he knew to be false (because deleting the blog is clearly effective as a protest and publicity stunt, and clearly ineffective in removing access to content that's been widely mirrored elsewhere already) in order to create the false impression that Alexander might be trying to hide something.
2. I consider knowing falsehoods intended to harm others to be ugly.
I thought you were disagreeing with (1), which is why I thought it's relevant that Alexander himself said his goal was that publicity, and that his actions seem consistent with his words. Are you saying that you agree with (1) but disagree with (2)?
I think that both the New Yorker reporter and Alexander know that deleting the blog will not meaningfully impede people from accessing it who want to access it. I think that the reporter's claim that deleting it might impede people looking for dirt in past posts and Alexander's claim that deleting it might protect his practice and his patients are both far-fetched although not completely impossible.
I agree that the primary benefit to Alexander from deleting his blog was in discouraging the NYT from publishing his name, and that his arguments for why it might still help even after he gets doxxed are much weaker. I'd tend to apply a more charitable standard to weak arguments for something he has the absolute right to do and that doesn't harm anyone else (what if he just didn't want to pay the hosting bill anymore?), than to innuendo questioning someone's character (by implying that this "creditable reason" might be out there) in one of the world's most-read magazines.
Assertion 1: deleting his blog is a meaningful way of hiding his surname, by way of adding an extra step to anyone who wants to search for it.
Assertion 2: deleting his blog is NOT a meaningful way of hiding gross and reactionary discussion happening on his blog, by way of adding an extra step to anyone who wants to search for it.
These seem contradictory to me. He is absolutely trying to hide or obfuscate something, we're just debating what it is.