Both Matthew’s and John’s Gospel narratives begin by focusing on Jesus’ roots—Matthew upon his human birth, and John about his divine origin. However, Mark begins his narrative with the ministry of John and Luke with John’s birth. Why is that? Perhaps, we can never know for certain, but I believe it may be to show that both Jesus’ and John’ ministries have divine origins. The difference being that John was fully human but his birth was ordered by God, and Jesus was God, himself, and ordered his own human birth. The prophets had predicted both the coming of the Messiah and the coming of the Messiah’s messenger, or he who would introduce the Messiah to his people, if not the world. As for why each narrative begins as it does, instead of another way or instead of all being alike, has probably more to do with the choice of its narrator than by human plan. Of course we cannot ignore the notion that the Lord inspired those choices, but that is another matter. We are speaking, here, from a human perspective, concerning why Mark / Peter did what he did and the other Gospel narrators did what they did.
Mark points to John the Baptist by referring his readers to the scriptures:
As it is written in the prophets, Behold, I send my messenger before your face, which shall prepare your way before you. The voice of one crying in the wilderness, Prepare the way of the Lord, make his paths straight. (Mark 1:2-3)
Mark says “it stands written” in the prophets… However, most ancient manuscripts say in Isaiah the prophet, and this is probably how Mark’s original account read, and in the prophets was a later “correction” by a copyist who thought he needed to correct an apparent contradiction, namely that Mark is quoting two prophets and seems to give Isaiah credit for both. Nevertheless, this is how many ancient Jewish teachers referred to the scriptures, when quoting more than one part of the text. They would use a key word or phrase that was used by all the accounts he had in mind, mention the dominant prophet, and his disciples were expected to know what he was doing. In the context of Mark 1:2-3 the key phrase is prepare the way which, appears both in Isaiah 40:3 and Malachi 3:1. Moreover, Mark quotes Isaiah 40:3 from the Septuagint (cp. Mark 1:3), but the text is applied to God by Isaiah—“prepare the way …for our God.” Nevertheless, Mark applies the text to Jesus, instead of God. To change the word of God in order to apply it to Jesus would have been inappropriate, and, no doubt, such a thing would have been challenged by Peter’s Jewish audience, so Mark’s record of Peter’s Gospel narrative in verse-3 is probably based upon an unknown ancient manuscript of Isaiah.
Isaiah 40:1-5 is all about the Jews returning from Babylon, and Malachi 3 is all about the coming of Elijah, the prophet. He was to come at the time of the end in order to turn the hearts of the Jews to the Lord before his coming. Moreover, just as Elijah appeared out of nowhere in the text (1Kings 17:1), without any explanation whatsoever, so John appears out of nowhere in Mark’s narrative without telling anything about him, when he was born or how he came to be baptizing in the wilderness. Also, Mark ties the texts Isaiah and Malachi together with the phrase prepare the way, but emphasizes Isaiah’s message about coming out of Babylon. In other words, from a spiritual perspective the Jews were still in exile. They had broken their covenant with the Lord, and he cast them out of the land and sent them into exile. They may have been brought back to their own land, but they had not come back to the Lord. Thus, preparing them to do so was the work of the Elijah, who had come, namely, John the Baptist. He brought them out into the wilderness where Moses brought Israel at the time of their exodus out of Egypt, but he couldn’t take them into the Promised Land. That would be done by another. The ministry of the Lord, Jesus, would be to lead his people out of Babylon and back to God, but John’s ministry was to point to Jesus—to introduce him to his people by preparing them for the way or, in other words, to follow Jesus.