Truman never wanted that. He flew around knowing that his nukes gave him an advantage over the USSR. From this paper, it is clear that Truman wanted to maintain an atomic monopoly and as for Joint Chiefs of Staff, they didn’t want to share the nuclear secrets with any organization including the UN.
That is an incredibly low bar to judge any organization. There are multiple conflicts going around the world that UN has done nothing to do. When it comes to permanent members of the Security council, the UN is powerless. Heck, it is powerless if one of the permanent members decides to flex it’s muscles somewhere else geographically either.
Also, no world war is also largely due to presence of nukes with nations. The concept of Mutually Assured Destruction prevents nations from going into full blown wars when 2 nuclear powers are involved.