The UN Security Council was created by the Great Powers after the WWII to ensure that the world would not go through a devastating world war again.
The Security Council has five permanent members – the great powers who defeated the Nazis, Japanese, and Italians. The non-permanent members are voted in by the general assembly.
In the real world, they use international binding laws to keep the world stable. They’re the collective security umbrella that ensures the world doesn’t become a nuclear wasteland regardless of political alliances.
The P5 does have power – they have complete Veto power over other member’s in the Security Council if the council chooses to go against their interests. Any P5 member, then, can do as they wish in the anarchic system, because the system was rigged for them because of the great victory.
Thus, it’s in Stark’s interest to have a UN-like supervision of the Avengers – he has the power and backing of the Greatest Power – ‘Merica and he can do as he likes as long as its under the interest of the United States of America.
True, you can’t constrain Thor or the Hulk, because they’re not necessarily humans, but Captain America can’t go about conducting a unilateral human intervention a la George W. Bush and accept everyone else to be happy.
In fact, Putin conducted the annexation of Crimea on the same grounds as Bush – Ethnic Russians were getting sidelined in the Ukraine and as the protector of everything Russian, he used the Russian Federation Military in the name of Humanitarianism to invade another sovereign country. smile emoticon
So take your pick –
Captain America is for American style unilateralism. The UNSC hinders Captain America so he will war if the need for war is just.
Tony Stark is in favor of American-led international alliances like NATO. The UNSC is useful as long as it helps Stark. Stark doesn’t think superheroes can regulate themselves very well so he wants to take charge and make them more precise and less deadly.