I have a couple of additional thoughts about my thesis that Matthew’s nativity story has a historical credibility that Luke’s story lacks.
First, Matthew knows accurate details about the historical situation following Herod’s death. He knows that Herod Archelaus succeeded Herod the Great in Judea, but that the realm was divided so that Archelaus did not control Galilee. This is the kind knowledge of events in a previous generation that Luke seems to lack.
Second, we know that Jesus’ brother, James, became leader of the Jerusalem church. Also early historians say that Jesus’ family continued to lead the Jerusalem church for another generation or so. This is circumstantial evidence that the family of Jesus had roots in Judea and that Jesus’ upbringing in Nazareth was a political expedient just as Matthew implies.