The way I heard it is that Luke and Matthew had Jesus born in Bethlehem for theological reasons. Being born in Bethlehem had prophetic implications.
The problem with English translations of the Bible is that English words don't always do justice to the original Greek. Logos has different shades of meaning in Greek. It can mean 'word'. But it can also mean principle or underlying rational reason. In Greek philosophy and early Christian theology, Logos meant a divine underlying principle to the cosmos.
Gospel of John comes across more philosohical and theological than the synoptic Gospels which never clearly indicate Jesus is coequal and coeternal with God the Father.
Yes, you're right, it is theology, not history