> If an AI model recongnizably regurgitates the essay it trained on then it has infringed.

I completely agree — that’s why I explicitly wrote ‘non-copy paintings’ in my example.

> The AI argument that passing original content through an algorithm insulates the output from claims of infringement because of "fair use" is pigwash.

Sure, but the argument that training an AI on content is necessarily infringement is equally pigwash. So long as the resulting model does not contain copies, it is not infringement; and so long as it does not produce a copy, it is not infringement.