I explain in blog posting (1) on this subject how and why the Gospels and Epistles were put in written form. It is important to understand and remember the concepts of "witnessing" that I explained and also the lack of written materials or a book orientation in those times.
This will also help you understand why the Qur'an was given to the Muslims in the form that it was given. The Qur'an was essentially a divine gift to "reconnect" the descendants of Abraham who were not Jewish with the God of Abraham. So the Qur'an is not like the Old Testament, which is structured in that it was an ongoing faith and historical document that was added to book by book over a period of many centuries. And it is not like the New Testament which is a witnessing of Jesus' arrival as Messiah, with what he said and did. The Qur'an can be thought of as the "all at once" giving of a bridge between Abraham and these of his descendants in order to provide an original and unique but fully valid and justified formation to their faith identity in the one God.
This is why it was given to the Prophet (PBUH) in the form that it was, to be memorized. The Qur'an was bestowed around seven hundred years after the death, resurrection and ascension of Jesus, but they were still times where knowledge was, for the most part, transmitted orally and there was not learning or materials for written documents. Therefore the tradition was formed of memorizing the Qur'an, as it was originally bestowed. Second, the Qur'an has a structure that is what one would expect if the purpose was to reveal to those who would listen and believe their religious legacy and heritage from the time of Adam to the present. The people who would become the Muslims were descendants who were not Jewish who branched off from Abraham, but without the legacy of faith history and codification of what God required of them in worship. And so God revealed to the Prophet (PBUH) what you might almost think of as a sampling of their faith history that they share with both Jews and Christians, but also new information. I say information because it is not as though the God who is revealing himself in the Qur'an is a different God than the one that the Israelites encountered or the Christians. But there is new information because God, through Gabriel, identified sacred places and filled in missing gaps that would be foundational to the Muslim faith as descended from Abraham. Then to the sacred material that restored knowledge of their heritage to the Muslims were given laws and forms to worship and understand God that were God's best choice for their cultural context.
Here is one way to understand it. Much of the Old and New Testament is written in a way that a pastoral people (herders of animals) can understand. God did not go about explaining what life was like and what he expected by using laws and natural concepts that only, say, Eskimos who live up north in the ice would understand. God, for example, didn't tell Moses to have the people sacrifice a perfect white polar bear to him plus some seals. I'm being slightly silly here but this is in help of making a serious point that many misunderstand. God knows and understands all, and he knows and understands the differences between various people and nations, and the land and culture in which they live. He should, of course, since he is the Creator and he is God. So God speaks to people, instructs them and establishes their worship requirements fully within the context of what they can understand and what their environment settings might be. To a pastoral people he speaks as a pastor and a shepherd. To nomads who live fully within pagan people he speaks as one who is more militant about establishing a reconnection with the one true God. Therefore God gifted the people who would become the Muslims with a reconnection to their religious legacy, understanding that Jesus was the Jewish Messiah and was a true Prophet, and a new set of laws and requirements for worship that are expressly relevant to fragmented nomadic people living within highly pagan and hostile settings.
This is why the Qur'an is very conversational in the sense of hearing the words of God. God provided the Prophet (PBUH) with understanding of God's trueness, oneness, power, all wisdom and all mercy through both instruction but also in an observational sense where through Gabriel the Prophet (PBUH) has an almost "inside" look at the extended faith family. Some of this has been misunderstood or overlooked, and I've written about that, and will probably do some more. But for now I'm just pointing out why the Qur'an has a structure and content that is both shared with the Jewish and Christian branches of Abraham's descendants and unique. The Qur'an is not like a Jewish sage who sat down and wrote a book of wisdom, or an Apostle who wrote his witness of Jesus' life events and teachings. The Qur'an is God's reconnection to the old and shared, manifestation of his identity that is a gift unique to the Muslims, and also the form of worship and law that would most benefit their family, cultural and real world settings and context.
I hope you find this useful. It is essential to meaningful ecumenical understanding to realize that the sacred scriptures have legitimate formation and content differences.