SPOILER WARNING: The significance of "253" and a possible explanation for Good Cooper's amnesia
""non-existence" could just mean the total wipe of good Cooper's memory, especially because he does not recognize Ronette as familiar in the big tin can room. "
He doesn't recognize Laura Palmer immediately, it's less likely he would have remembered Ronette's face, so the idea this causes his catatonic state doesn't fit well with me. I think the AC/DC theory for why Coopers brain/memories are scrambled. The non-existence line, for me, seemed to indicate a more metaphysical threat, than any real action by the doppleganger. Cooper is also somewhat coherent for the scenes following falling through the void, so it seems even more unlikely that the Doppletree did anything to him mentally or physically, apart from sending him into said void.
Also, even the end credits haven't confirmed that this is Ronette, so we can't ask for Coop to do it.
I agree that it is metaphysical, but also "thrown" as a kind of curse.
Another reference to non-existence is when Mr. C asks Jeffries, if it is Jeffries, on the phone "Are you nowhere?"
yes that is what I think too.