In the story "The Legend of the Three Brothers", Death gave the Elder Wand to the eldest brother, the Resurrection Stone to the second eldest brother, and the Invisibility Cloak to the third eldest brother.
In the story of "Harry Potter", Dumbledore gave the Invisibility Cloak to Harry and the Elder Wand to Voldemort, so would he have left the Resurrection Stone to Snape?
If in the story, all Dumbledore did to Snape was just tempering and testing, and he left Snape with the possibility of truly realizing his wish, how would the story develop?
Dumbledore said: "I'm sure. I trust Severus Snape completely."
Purpose: Change and Trust