> I can write a poem in my head without ever writing it down on paper. I still wrote a poem, even if I just pass it along orally
This is generalising the term writing to the point of uselessness. In your example, you thought of a poem and spoke it. You didn't write it.
I don’t think so. The colloquial usage exists as grandparent commenter describes. I can be a “songwriter” without literally writing the lyrics to my song down.
Disagree, I think it's analogous to how we today use "fire" to describe the action of loosing an arrow or whatever the technical term is for a trebuchet, even though neither has gunpowder.