The organization that didn’t exist until after WWII?

The organization that isn’t responsible for deciding where the Olympics are held?

And as far as stated primary goals:

United Nations Charter, Chapter I:
Purposes and Principles

Article 1

The Purposes of the United Nations are:

1. To maintain international peace and security, and to that end: to take effective collective measures for the prevention and removal of threats to the peace, and for the suppression of acts of aggression or other breaches of the peace, and to bring about by peaceful means, and in conformity with the principles of justice and international law, adjustment or settlement of international disputes or situations which might lead to a breach of the peace;
2. To develop friendly relations among nations based on respect for the principle of equal rights and self-determination of peoples, and to take other appropriate measures to strengthen universal peace;
3. To achieve international co-operation in solving international problems of an economic, social, cultural, or humanitarian character, and in promoting and encouraging respect for human rights and for fundamental freedoms for all without distinction as to race, sex, language, or religion; and
4. To be a centre for harmonizing the actions of nations in the attainment of these common ends.

Nothing about representing the whole world. How would it even do that? Take a vote on the world’s favorite ice cream and the winner is the world’s favorite?

a lot of people use "the UN" as a sort of shorthand for "all the countries of the world".

No, no they don't.