The desire to force new employees to sign agreements in total secrecy, without even being able to disclose it exists to prospective employees, seems like a pretty negative “value” under any system of morality, commerce, or human organization that I can think of.

That's a perfectly fine belief to have. I might even agree with you. But you're not really advancing a discussion thread about a company's strong ideals by pointing out some past behavior that you don't like. This is especially true when the behavior you're bringing up is fairly common, if perhaps lamentable, among U.S. corporations. Anthropic can be exceptional in some ways while being ordinary in the rest.

(I have no horse in this race. But I remain interested in hearing about a former employee's experience and impressions about the company's ideals, and hope it doesn't get lost in a side discussion about whether NDAs are a good thing.)

Lots of companies do it. Doesn't make it right, but HR has kind of become a pretty evil vocation, these days. I don't believe that they necessarily reflect the values of their corporations. They tend to follow their own muse.