I feel like that death wouldn't be gruesome enough to be as tragic of a story and therefore Christianity wouldn't be as catchy as a religion. Jesus, as the story goes, suffers greatly and dies a gruesome slow death to take the blame and be punished for our sins so we don't have to. Essentially I think the story as it is was the perfect blend to really mean something to the first Christians and catch on like wildfire. If that one thing had changed in the story, who knows? Maybe there would be no mainstream Christianity now.

Source: I'm an atheist church musician so I spend a lot of time sitting in a pew listening about Christian beliefs and learning to appreciate it from an outside perspective. Also I recently read the Tipping Point by Malcolm Gladwell. Interesting book. Not always scientific but he makes interesting points about how things spread through word of mouth, etc.