We need to remember that the primary and most important purpose of the UN was and is to prevent international war, period. Domestic stuff is domestic stuff and the UN really has no place in it, under the current Charter.
That being said, I think the NATO invasion of Yugoslavia and the coallation invasion of Iraq is proof positive that the Charter as it is no longer viable. It's no going to work if nations keep ignoring it.
"What benefits do we, and the world, derive from the continued membership of the United States in the United Nations?"
The world UN gets a the world's army from time to time when the US decides it wants to support a SC resolution calling for members to enforce it militarily. Is this worth the cost of having the US ignore others and break the charter? I'm not sure. The UN also gets the US's significant dues, when the US decides to pay them.
The US gets a hell of alot out the UN. The veto for one. Which is great because that means the UN can never sanction the US no matter what it does. And because the UN is primarily located in New York. It makes it very easy for the US to spy on the members there.