The point of citing sources is so that the reader can retrace the evidential basis on which the writer's claims rest. A citation to "Chat GPT" doesn't help with this at all. Saying "Chat GPT helped me write this" is more like an acknowledgment than a citation.
Again, it is standard practice to cite things like (personal communication) or (Person, unpublished) to document where a fact is coming from, even if it cannot be retraced (which also comes up when publishing talks whose recordings or transcripts are not available).
> I always acknowledge ChatGPT in my writing and never cite it.
These are not the uses with which I am familiar—as Fomite says in a sibling comment, I am used to referring to citing personal communications; but, if you are using "cite" to mean only "produce as a reproducible testament to truth," and "source" only as "something that reproducibly demonstrates truth," which is a distinction whose value I can acknowledge making even if it's not the one I am used to, then your argument makes more sense to me.
