> These arguments about why we're all obligated to cooperate with Alexander's attempt to walk his identity back always seem to be inventing new norms
Not really. The NYT was perfectly willing to protect the anonymity of a different psychiatrist blogger. Yes, this person did a better job of keeping their identity a secret, but the justification was largely the same.
And let's not pretend that journalism is only about sharing information. There's a great deal that journalists don't share (or even try to actively suppress) for many different reasons. Partly because there are a lot of ethical considerations when publicizing information.
Worth noting that part of the issue is that, with psychiatry and counseling in particular, it really doesn't matter what he was writing about or what his politics are. Any such publicity compromises the blank slate that counselors are supposed to present to their clients. While this does mean that mental health professionals have an obligation to take care with their public image, it's not unreasonable to ask others (including journalists) to respect the particular cost they face with any kind of exposure.