Question: Why did the other disciples who traveled with and followed Jesus not write a Gospel?
AP: In a group of apocalyptic fanatics who were convinced that the end of the world would come immediately (both Jesus and Paul), it makes perfect sense that they would not try to write anything about the teacher. Moreover, once they were convinced of the truth of his resurrection and appearances, the master was spiritually alive among them and Christian prophets, indwelt with the spirit of Jesus, transmitted his words to them. For these reasons, they would have felt no need to write anything.
TWH: Matthew writes the first Gospel shortly after the resurrection and ascension of Jesus. It is reasonable to imagine that he wrote this Gospel in collaboration with the remaining apostles while they were all still in Jerusalem. Oral instruction was very important. It always has been. But the written text has been as well. And the apostles understood that they needed (1) a faithful and accurate record of the life, works, and teachings of the Messiah that (2) was capable of persuading their primary audience, which was Jewish, that Jesus was indeed the long-awaited Messiah. We get additional Gospels as the message of the cross spreads throughout the known world. Luke writes his Gospel as the message of the cross begins to engage the Gentile world more and more. And Mark comes to us by way of the preaching of the apostle Peter in Rome, not because Peter sat down to replace or write a whole different Gospel. And John, some years later, cannot imagine drawing his last breath and not leaving a record of some very important events in Jesus' life, such as the miracle at the wedding in Cana (John 2:1-11) and an extensive account of Jesus' teaching the night before he is crucified (John 14–17). That's the human element for how we get the Gospels that we have. But there's also a divine element. The individuals wrote these Gospels because they were led to do so by God. They were prompted to do so because writing these Gospels was part of "laying the foundation" of the church (Eph. 2:19-20). The writing of the Gospels was part of what it means to "hand down" the faith once for all (Jude 3). Could there have been an additional Gospel? I believe there could have been. John even tells us as much in the Gospel that he pens (John 21:25). But in the sovereignty of God, we have four faithful and accurate witnesses to the life and mission of the Messiah, and they are Matthew, Mark, Luke, and John.