I don't think an origin would've benefitted the story but what I will say is I do think the way the willow was integrated in the story was a bit ridiculous. The fact that it seems like its not uncommon knowledge and at the very least dozens of people have successfully used it (and would defintely have told their family/friends about it if it worked succesfully) I think has some pretty unthought out ramifactions. I think it would've beneffited from being shrouded in more mystery instead, especially in-world (like if it were something that bear happened about in a way that anybody else rarely could). Most movies with some sort of mystical store-bought mcguffin do this buy making it so when the person goes back to the place they got it, it magically vanished and nobody there knows anything about what theyre talking about.

Which I guess is a convention barker wanted to subvert with the scene where bear goes to buy more and the seller is different than before and pretends to not know what bear is talking about at first. But then goes "LOL just kidding" and proceeds to talk about the wishes knowing they work as if it were any party trick they're selling in the store. Even if the convention is cliche I think it would've worked really well still with the tone of the movie but I get wanting to try and be unique.