Not only would material burdens be shared, but even more importantly, the burden of exercising power would be shared. The exercise of power would be legitimated in the eyes of the world, or at least within a substantial body of world opinion, if actions were taken, and seen to be taken, not merely as a naked exercise of American power in pursuit of American interests, but with the consent and by the authority of other nations as well.
This has been very nearly the case in the current war in Iraq. Although the US news media speak grandly of a "Coalition" -- a term that evokes the first Gulf War of 1991 -- the only significant military contingent, apart from the American forces, is British. Some Australian special forces are involved, and purely token representation from a handful of other countries. While the British contribution is substantial, even it is somewhat in the nature of a fig leaf over what is effectively a unilateral American action. In short, the United States has the means to invade Iraq and depose the Saddam Hussein regime, and is militarily capable of doing so whether it has any support from other countries or not.
The Concept of International Legitimization
This financial dimension aside, the important and fundamental thing about the first Gulf War is that it was not, in its political dimension, an "American war." It was a global effort. Authorized by United Nations Security Council resolutions, it was carried out by a coalition of nations from within the Middle East region and around the world, including major regional and global powers.
In any case, cooperation was half-hearted, and the United States has in fact invaded Iraq, in spite of failing to secure a follow-up resolution authorizing the use of force. It may be argued -- and with considerable validity -- that the United Nations has been substantially weakened by this entire series of transactions. The Americans secured a United Nations mandate for renewed inspections,