SatansMaleVoiceChoir
Illuminator
You don't have to believe the stories (I don't ) in order to investigate when they originated. And while there's some discussion on the dating of the gospels and Paul's letters, the disagreement is in a couple of decades rather than centuries. AFAIK, there is no controversy at all about the age when Muhamed lived.
If you have an interest in the origins of myths and legends, or biblical scholarship, then I would imagine it would be interesting and worthwhile to be able to date these stories, yes.
I absolutely disagree. First of all, there's little controversy that an actual Nicholas bishop of Myra actually lived in the 4th Century, and is the basis for the Dutch Sinterklaas figure. Secondly, even if they're made-up figures the question where and when they originate is interesting.
Again, if that interests you then that's perfectly fine. But my point was that comparing the age of two works of fiction as if this would add some sort of truth value, or credibility over the other, is ultimately pointless.