The point is to have a dialogue and to allow the largest influences to shape the dialogue. It's not meant to have any power beyond diplomatic conversation. The most hostile countries to the US still get in a plane and fly to New York to participate. Think about that.

Because getting small countries to stop helps reduce war deaths.

To allow the big countries a place of communication to prevent wider conflict.

I think once the US and EU realize that the "Unipolar moment" is fucking over we'll get a lot more use out of the UN.

Cool, in the EU all countries have veto power. In the UN, all permanent members of the security council have veto power. You just need one of them to refuse to give up that power. In the EU, I believe this could somewhat work, but in the UN ? No way the US, China, Russia, France or the UK would give it up without leaving the institution.