Why didn’t Paul quote Jesus more often?

Readers of Paul’s letters have often wondered why he didn’t quote Jesus’ teaching, or refer to episodes in Jesus’ ministry, more than he does.
In The Historical Reliability of the New Testament, Craig Blomberg suggests a number of factors that help to explain this:
First, we must remember that none of Paul’s letters represents first-time evangelism of unsaved people or even the beginning of the discipleship process for brand-new Christians. These had already taken place before Paul ever penned a single one of his epistles. Rather, Paul is addressing specific problems in the churches to which he writes…
Second, none of the rest of the New Testament epistles has any greater frequency in using the Gospel tradition of Jesus’s words and deeds…
Third, following from these first two points, early Christian epistles were apparently not the preferred genre or context for catechetical instruction about the life and teaching of Jesus. This occurred by word of mouth, as preachers and teachers orally passed on what they believed people needed to know…
Fourth, …Jesus’s followers quickly recognized that the most important features of his life were his death and resurrection…
Fifth, the sense of divine inspiration or guidance that Paul experienced would have freed him up to write in the words he sensed he was supposed to use…
Sixth, on more than one occasion Paul has to stress that he has as much authority as the apostles in Jerusalem do, against those who doubt or oppose him (esp. Galatians 1–2; cf. Acts 15)…
(Emphasis added)