I dont think this is a zero sum equation. Clearly when you have multinational forces working togeather there are diverese goals. Having a unified command is very useful and the problems of international military HQ's and Armies have been studied in depth. The question really is what the different groups get out of their partnership, some allies have hurt their partners in wars while others are helpful.
The US speant a lot of money on Australian and Korean (among others) forces in Vietnam.
As it is the US is doing most of the work and spending most of the money in Iraq and A-Stan but the contributions of the other countries should not be overlooked.
The military contractors in Iraq can make $1,000 a day. Wars cost a lot of money. Clearly after the Americans the military contractors and then the British are making the biggest contribution but I think that America's $200 million on allies is better spent money than some of the weapons they develop and produce.
Just my 2 cents
cheers