Moshe Rabbenu said to Yisro, ki yihye lohem dovor bo elai, if they have a concern, he comes to me. It should have said, boim elai, they come to me? The Chasan Sofer explains that he was saying that their problems affect me. It comes to my heart, so I have to act on it.
The Dubner Magid says that they are two kinds of din torahs. One, where one goes to make sure tbat the other did not take something away that he thinks belongs to him. Another, where he wants to make sure that he did not take somehing away from the other. In the second case, as he is arguing for the other, the other does not have to show up at the din torah, therefore only one party will come to argue for the other. This is the meaning in Pirkei Avos שלי שלך, שלך שלך, חסיד mine is yours and yours is yours is a pious person. If he says mine is yours then certainly he wil say yours is yours? If there a question to whom something belongs, he is willing to forfit it because he wants to be sure that he does not take anything not belonging to him.
Maybe that is why Moshe Rabbenu did not follow Yisro’s idea on his own. These people are careful with the other’s money, so how can he allow to rule by someone other than him who have not heard directly the Torah from Hashem.