To answer your first question "Does the client need to crawl from the root node down to a nested resource to just make a POST if it doesn't know the direct URI?"
The answer is No. The client always does not have to crawl from the root node. It is possible to design the URI;s such a way that the navigation to reach the direct URI can be from other views. For example if the purpose of the URI (/Products/product1/Delete) is to delete product , then it should be possible to reach this by either crawling from the /Products or by giving a namespace query of Products/Deleteview. This "DeleteView" URI should give all the URI's of the delete view. i.e it can return a uri collection like Products/product1/Delete, Products/product2/Delete etc.
To your second Question "What would be the purpose of API documentation then?"
Concept of API is a legacy of the past. Ideally the URI itself should be the documentation. This way the client can be programmed to discover and take only things that it can respond to.
We got hold of unique technology which manages these namespaces. so we are shielded from this view manipulation ourselves. I recommend using a technology to manipulate and create these URI namespaces.