But your bulleted list is an incorrect entailment of what "a function at its core" means wrt OP, Elm, or Bernhardt's talk, so it seems more like you're reacting to your own reductio of what that quote could entail.

You haven't explained what is wrong with using a pure function to model state changes in an application. To do so, I think you'd also have to contend with the fact that a solution like Elm works quite well in practice.