Why didn't they make this an American struggle from the get-go, and then later welcome the assistance of anybody who wanted to get on board with us?
This is the worst place in the world for us to get into a war. Britain and Russia learned that the hard way.
Absolutely correct. I'd rather go into a fight alone or with one or two reliable friends than with 20 people that don't want to be there, or with one or two who want to stab me in the back. Even if no "partners" in a coalition are Trojan Horses, the coalition approach undermines unity of command (one of the maxims of war) and brings things down to the least common denominator. Napoleon rejoiced when he found his enemies had formed a "coalition" because he recognized that this coalescence of states with different interests created fault lines that he could--and did--exploit. At this time, that is a recipe for disaster. We need unity of purpose, unity of command, and the will to win. A broad coalition will give us none of these things.
Because we don't own any real estate in the entire region, so country we occupy without their permission, we would have to invade and subjugate first.