If the amazing events surrounding the birth, life and death of Jesus were merely isolated miracle stories like a Greek legend, perhaps we could dismiss them more easily. But Luke and the other New Testament writers show that Jesus fulfilled prophecies about him that were written down hundreds of years before he was born. There are hundreds of prophecies and allusions to Jesus in the Old Testament, and he fulfilled them all. Including ones that humanly speaking he had no control over, such as Isaiah 53, which tells the manner of his death. Let's get back to the shepherds.
Reality is scary.
The angels show us that reality is more than the material world. A material world is comfortable because we can understand it. To some extent we can control it. But angels are uncontrollable. They are scary.