These are all valid points. I wish I had time to really explain, but I simply want to make two statements:
1) I have no dount that the Nephites were quite familiar with the importance of Bethlehem, as clearly there was a great deal of historic and messianic importance to the city. However, their familiarity with its actual location is quite understandable in my mind. Moreover, this chapter is a sermon delivered to people in a city that is rather new to the gospel of Christ by Alma, the leader of the Church at that time. It would be even more lamentable that they did not understand the messianic prophecies that Alma lays out for them. He speaks to them as if they are quite naive to the nature of the Christology already had among the Nephites, and he mentions that there was even some waywardness among the people. Such a people would likely be ignorant to the full significance of Bethlehem in my mind.
2) I appreciate your last statement about not trying to pick a fight, but I didn't even suspect it with you. I wish to make it clear that I don't detect any condescension in your tone, merely an effort to explain and possibly correct what you perceive to be in error. I can handle tough questions without a problem, but I don't appreciate what appears to be talking down. I got no such vibe from you.