Why do Christians become Christians?

[TheRocketSurgeon]

I think this comparison shows that you need to look into a little more what you are talking about.   It is not like the game of telephone at all.  For one, the information is not passed one at a time in series, without the others knowledge.  Much like here, if I where to make a mistake in a quote I made of you, others could chime in, and correct me.   There is corrective feedback....  Anthropologist, have shown, that cultures who rely strictly on oral traditions /transmission, can be very accurate, even in very long stories that take quite some time to tell.  

I think you're quibbling more than a bit with the details of how storytelling works, here. Yes, there is corrective feedback, but there's also input from so many sources, as the story is told and retold by the traveling men (the "Disciples"), and spread by those they told.

And the phenomenon you're discussing, which "anthropologists have shown", is more to do with how the Genesis stories survived, relatively intact, in the oral tradition prior to the invention of Canaanite writing and/or the actual writing of Genesis. Specialists (priests, shamans, etc) would memorize the stories, intact, and repeat them with surprising fidelity. That has little to do with the type of myth-building we see active in the Mormons, for instance, wherein several variant stories (with each retelling) get "corrected" back to a coherent whole only after myriad permutations emerge, and by comparing the result to actual records, we can plainly see and trace the trail of bullshit-- yet many people, including recent Presidential candidates, are Mormon.

They could have always asked Mary the mother of Jesus.  
Also, I don't think what you imagine, corresponds to history, and the disciples of Jesus geographic dispersion after Jesus's death.   Not to mention, the studies, that show that it takes generations for legend to replace the facts of a culture.  I'm also finding it difficult, that these separate groups would so quickly go from the rapidly changing stories that you propose, to come to an agreed upon version and rejecting that which differed so quickly.

You don't think it's plausible that, in an attempt to sell others on the legend of their teacher, they began to rely more heavily on the "signs and wonders" claims, which start out rather tame in James (and possibly Q), which are simply collections of his sayings (little to no magic), then increasingly added to the legend through Mark, Matthew, and Luke/Acts, until blowing up out of proportion a generation later, with John? You really don't see how the game to win converts to their new ideas might have altered the story somewhat?

We can follow the alterations made to the legends, through time, now. It's as plain as the nose on your face.