That’s a common idea but I don’t think it holds up to scrutiny.
Putting poetry to music has a long history: see Homer, for example. And I don’t think there is much continuity between people that were writing poetry who later started writing rap. Different worlds, different audiences.
I do agree that some of the cultural desire for complex and creative language-play definitely is met in hip hop and rap, though.
I don't think poetry morphed into rap, rap is poetry. It also happens to be the most popular type of poetry now.