What was the Need for Writing the Gospels
Christ Jesus had at least twelve disciples. Each of them could contribute to establishment of a unique gospel, although most of them could not read and write.
As Christ Jesus acted for His missions in this world for three years, there must have been about 1,000 episodes. Each disciple could choose any of them for his gospel. So, such gospels should be vastly different from one another, if each gospel would have contained about 100 episodes.
If early churches had seen two different types of gospels, what would they have? They would try to merge them but also discard minor episodes from both of them to make a new gospel concise. As they had to respect both the disciples or authors, the resultant new gospel would not be biased to any of them.
But the common part among Mark, Luke, and Matthew constitutes 76% of Mark's contents, 46% of Matthew's contents, and 41% of Luke's contents. The common parts between Matthew and Luke occupies 24% of Matthew's contents and 23% of Luke's contents.
(https://en.wikipedia.org/wiki/Synoptic_Gospels#Common_features)
They heavily depend on Mark. In addition, it looks as if each of Luke and Matthew was made out first by merging each other into each and then by merging Mark into each. Apparently Mark was positioned above Luke and Matthew.
Strangely, there are no other authentic gospels except John. It looks as if there had been no other authentic synoptic gospels. But because there were 12 candidate sources for gospels and 1,000 episodes of Christ Jesus, there must have been more synoptic gospels with different selection of episodes of Christ Jesus.
It means that there was a specific need for a disciple to write a gospel. And special conditions were needed for a disciple to write a gospel. But as only three synoptic gospels were authorized, the need must not have been related to existence and deployment of Christianity in general terms in the last half of the first century.
Put simply, the need was fist found by the author of Mark. And then, Luke and Matthew realized it. It also suggests that these authors must have been living in a specific location or a city. Therefore, these gospels must have been established around Rome to avoid persecution of early Christians by the Roman authority.
Yet, it is also apparent that these authors did not intend to have their gospels adopted as holy books of Christians on par with the Old Testament or the Jewish Bible. For early Christians, their holy book was the Jewish Bible. They could not claim that they had authority to write Christian bibles. Nonetheless, there was a need for them to write gospels. The reason must be related to the need to avoid the persecution of Christians by the Roman authority and, especially, the execution of St. Paul and St. Peter.
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Mar 1:22 And they were astonished at his doctrine: for he taught them as one that had authority, and not as the scribes.