Note: We are passing over a large amount of material duplicated in Matthew and Luke.
There is nothing in this passage offering a hint to the legal status of the estate the man asked Jesus to arbitrate. The most common case would be when one heir tries to keep an estate together and share ownership with the other heirs under the claim that it would be far more valuable to all of them if kept intact. If this were the case, Jesus’ response makes a lot more sense.
The man was asking Jesus to use His influence, but it implies making some kind of judgment about the disposition of property. The man was asking Jesus to support his side in the dispute. The issue was not divine justice, but petty rivalry and greed. Jesus denies having any jurisdiction in the case, but then goes on to explain why He has no interest in such things.
He turned to the crowd and told the parable of the Rich Fool. What made that man a fool? He was self-centered and short-sighted. The whole purpose for which God grants prosperity as a covenant blessing is to share with one’s family. The Law of Moses was a tribal covenant, not an individual covenant — a tribal feudal nation. As part of the Hellenization, there was an emphasis on the individual that did violence to the Covenant. Your typical wealthy Pharisee would simply hoard this wealth and look for ways to deny even his own parents. The whole idea of the Covenant was to make Israel a single nation, united in sharing the blessings of shalom as one people. This is not communism, but tribalism, and the details of the Law required it.
If a wise man prospers, he immediately seeks to distribute his excess in ways that really do bless people by encouraging holiness. He discerns the real needs and invests in the future generations to make his nation righteous. He wants to be found faithful when his time in this world ends. Granted, the Law demands that men seek to lay aside an inheritance for their heirs, so they come first, but the man in this parable was thinking only of his own personal comfort. Apparently this is the case of the man who asked Jesus to arbitrate for him.
Thus, the parable ends with the solemn question: “Then whose shall be those things which you have prepared?” Who was supposed to get that stuff in the first place? If you have no plan for passing this stuff forward to your kin — your responsibility — then you are a fool. And if not your own kin, there will always be needy folks in your vicinity who would bless the Lord for your generosity to them. But the whole purpose God grants prosperity is for the glory of His name.
Would Jesus’ judgment in the arbitration here be binding. As in, would His decision as a rabbi hold weight in the matter? If so, interesting bit of history there, that preachers could have that kind of power (not that the Roman occupiers would necessarily see it the same way).
No, the man was asking Jesus to use His influence. There’s no reason to think a rabbi had any legal authority, but they may have some influence on the court, rather like a strong “friend of the court” brief.