Indeed. In my view, "software engineering is a solved problem" is a roughly equivalent statement to "writing is a solved problem." I'm convinced that people who say this were never serious engineers to begin with, viewing code entirely as a means to an end.

To me, code is both the canvas and deterministic artifact of deep thinking about program logic and data flow, as well as a way to communicate these things to other developers (including myself in the future). Outsourcing that to some statistical amalgam implies that the engineering portion of software engineering is no longer relevant. And maybe it's not for your run-of-the-mill shovelware, but as a profession I'd like to think we hold ourselves to a higher standard than that.

Also, does the sum total of software engineering done up to this point provide a sufficient training set for all future engineering? Are we really "done"? That sounds absurd to me.

I think people spouting absolutist statements like "software engineering is a solved problem" should largely be ignored.