What is global leadership? Because of European history at waging war upon itself it has eschewed further military adventures generally. The United States, Russia and China were more or less on the same anti-fascist side during W.W. II and each has carved out a sphere of influence or formed trans-national alliances and ad hoc networks. Each has used military power abroad on a few occasions. Europe has provided some military forces to joint American or U.N. ventures yet not made the sort of commitment to defending freedom militarily that the United States has.
Global leadership may be defined in several ways; technology, military, human rights, environmental restoration to health, space exploration, standard of living for ordinary people and so forth. In my opinion world leadership is a kind of mixed bag. It might even be possible to recognize African Christian increase as a form of world leadership.
It is possible that the world leadership appellation is vain. Those that make the world a better place for ordinary people are from virtually every nation. Those that keep it free and those that would oppress individuals for elitist governments also are found across the globe. Plainly not enough is being done by any government leadership to say that anyone is leading effectively in a good direction such that people would overwhelmingly want to follow.