The question asked here is as follows:
Is there any scholarly analysis of why more of Jesus' of sayings involve the rich rather than the poor?
One comment regarding this question is as follows:
This question appears to be off-topic because it is about God's motivations.
Jesus wore his motivations on his sleeves, so to speak. He spoke of his and his Father's love and care for their errant children. He told people clearly that the reason/motivation for his coming into the world was to seek and save lost people. He revealed his tenderness in some of his "I AM" statements, such as "I am the good shepherd," and he encouraged the weary and heavy laden people to come to him to find rest for their souls.
He wept over Jerusalem and said explicitly why he was doing so. He wept at Lazarus' tomb. In the Tanakh God laid out very clearly and in many places that his motivation for giving his people his Law was for their blessing, their shalom, their satisfaction and fulfillment (see, for example, Jeremiah 29:11). I could go on and on and on.
God's motivations are interspersed throughout all Scripture, and to say God's motivations are inappropriate or off-topic for this website seems, well, ludicrous.
Granted, the question would be difficult to answer, and it cannot be answered without careful study and without taking a meta approach to Jesus' teaching style, which approach is inherently risky, perhaps. On the other hand, Jesus took a meta approach to his teaching, particularly when it came to his use of parables and opaque sayings, which he characterized, in part, as deliberate obfuscation (see Matthew 13:10 ff., and Luke 8:10)! Combining that insight with insights gleaned from what other passages throughout the gospels and the rest of the Scriptures have to say about the rich and poor, a person could tease out at least some tentative theories as to why rich people figured more prominently in Jesus' communications as delimited by the OP.