Well, people who voted for Labour in the GE have a right to be represented. Labour has a duty to represent them.It's not but the question is how do you decide? The Labour party is set up to allow the members to have a huge say in the party's direction and I don't think people are voting Corbyn because they think he will benefit them personally.
And, I totally disagree with you on your last point. People voting for Corbyn do personally benefit from it. Sure, they don't receive a payment for it; but they share his views and it is them he speaks for. I just think as party leader it is his duty to speak for other Labour voters too. I do not think he thinks it is, though, which is why many think he is an incompetent leader. One would imagine an important aspect of being a party leader is to represent all your supporters as much as you can; not just your most loyal supporters.