But writing, calculators, search engines etc. are specific tools, you drop a skill to gain effectiveness in another. While AI is a general tool whose builders intend it to be able to perform all cognitive work. Past a certain point, what is left of the human?

I do not agree that the concept of writing can be considered a specific tool at all. Maybe a pencil, but writing opposed to remembering everything is a more substantial level of a paradigm shift than AI use is.