The answer I have most commonly heard to this question is that the earliest Christians were too much on edge expecting the return of Jesus any day to be bothered or to see any need to write down the things they supposedly heard Jesus did and said.
But the odd thing about this explanation is that so many scholars like to date the Gospel of Mark as early as 70 c.e., in the midst of the Jewish-Roman war, during the siege of Jerusalem. That is, precisely at the time when the return of Jesus would have been the MOST expected any day or hour.
Some even like to date this first gospel earlier, to the 40’s c.e. when Caligula attempted to have his statue placed in the Jewish temple. Again, one would have expected even more apocalyptic fervour that much sooner after the supposed events of Jesus’ death and resurrection.
It’s not as if there were no literates among the converts all those decades. If we take the letters of Paul at face value then we see evidence of a number of individuals with scribal skills.
Given the astonishing deeds and sayings earlier believers attributed to Jesus, it beggars belief that no-one would not have been interested all those decades to be among the first to commit them to writing.