He showed considerably more respect for them and the principles underlying both the U.N. and the United States in his remarks to the General Assembly. However, while they were generally well-received, the central headline-grabber in his speech was a promise to stop Iran from getting nuclear weapons, something that neither he nor anyone present in that chamber today may actually be willing or able to do.

This leads in turn to the also important point that the president of the United States may no longer be the most powerful man in the world. That is not because the United States is not the most powerful nation in the world — it still is. But rather, it is because the president can’t seem to get much done in Washington; Congress has become a roadblock for executive action of most sorts; and whereas the president can take independent action in most instances, the United States lacks the will or the resources to project force or use soft power elsewhere in the world. Thus, even the job of No. 1 world leader ain’t what it used to be.

Beyond the nuttier dictators of this world and presidents of countries that are bound like Gulliver in Lilliput by the limitations of their own national bank accounts and flawed political systems, there are others flaunting the world leader label in New York this week who also provoke questions about their legitimate claim to that title. From Benjamin Netanyahu, whom very nearly no one is likely to follow, to Egypt’s Mohammed Morsi, whose control of his country is as ambiguous as is his cloudy view (shared by Obama) of the U.S.-Egypt relationship, from Pakistan’s Asif Ali Zadari to Afghanistan’s Hamid Karzai, the U.N. is awash in political figures who face such serious problems back home that real leadership would have suggested they pass on this week’s opportunity to hobnob over canaps at the Waldorf.

So, to recap: Some of the leaders in New York this week aren’t actually the leaders in their own countries. And others are not really considered important players by their peers. Still others are seeing their ability to lead diminished or constrained. And above and beyond these factors is the reality that the secret to being a world leader is not so much having a vision or a title or a big army, but getting other people to follow you.

Given the U.N.’s recent record of inaction on vital issues from Syria to climate change, the one thing these so-called leaders have proven beyond a reasonable doubt is that motivating followers and energizing alliances is not their strong suit.

There are, we should acknowledge, real leaders out there — people creating new jobs, overseeing the development of new technologies, curing diseases, solving big problems. They just don’t happen to be the people causing most of the traffic jams in New York this week. So perhaps if we can’t get these people in town for the General Assembly to actually lead, we might do the next best thing and stop calling them what they are clearly not.

David Rothkopf is CEO and editor at large of Foreign Policy.