How would Stockton's "The Lady, or the Tiger?" be different if readers learn what is behind the door indicated by the princess?

The whole magic behind Stockton's story "The Lady, or the Tiger?" is that the ending doesn't tell the reader which fate the princess's lover receives. The story thrives on the ambiguity left in the wake of a compelling tale. If readers discover if a lady or a tiger emerges from the door indicated by the princess, then nothing would be left for readers to decide after reading it. The narrator leaves readers with the following:

"The question of her decision is one not to be lightly considered, and it is not for me to presume to set myself up as the one person able to answer it. And so I leave it with all of you: Which came out of the opened door—the lady, or the tiger?" 

The narrator says in the above passage that since the lover's fate should not be taken lightly, the narrator shouldn't be the one to reveal the princess's decision. As a result, the author/ narrator hands over the decision to readers, which empowers them to decide the ending of the story.
On the other hand, if Stockton just allows the narrator to give up the ending, then readers would not enjoy the internal debate that can exist in their minds afterward. Furthermore, readers would know for sure if the princess would rather see her boyfriend married off to someone else or die a horrible death by a tiger. The character of the princess would be decided, and no other discussion about the story would take place. Either the princess would be crowned a selfish girl by allowing her boyfriend to be eaten by a tiger, or she would be considered a loyal lover who would rather see her beloved happy in another's arms than with her if it meant that he lives.
The story lingers in readers' minds long after reading it because of the ambiguous ending. This is the magic of the story. The fact that readers are empowered to decide the ending gives it an original quality rarely found in other stories.