The ending of Heaven's Feel is meant to mirror the start of the story.
The same fire filled environment created by the same creature and the same near death experience in both cases. But this time around Shirou constantly tries to avoid becoming the bone of his sword and talks about how much he wants to live instead of how much he wants to die.
You can also say that Shirou's origin has always been swords, even before the whole fire trauma. But that doesn't change that his mentality and body actually comes from that whole life changing moment. It's Kiritsugu who puts Avalon inside of him which increases his sword affinity and connects him with Saber, who represents the beautiful heroic ideal he wants. And in the end he kills her with his own hands and the body that had Avalon disappears. In the same route where his ideals are abandoned.