In "The Scarlet Ibis," why do you think the narrator chooses not to return to the present at the end of the story?

There are two reasons why the author stays in the flashback.   The first reason is because the story 'dies' with Doodle. Everything ends under that tree: Doodle's life, the author's innocence and our glimpse into their life.  And it's a powerful ending because as the reader you're left with the image of Doodle under the tree.

That's the second reason for the story ending in the flashback.  You understand fully that this is the image the author has carried with him his whole life.  This knowledge makes the story more sad and delivers the 'pride can be evil' theme more powerfully.