to take all the points one by one
Von Adler... there are 100 million Mexicans actually, not 40 million.
Gustavas, my point is that you don't have to occupy the world. At least not for a long time. You break the back of possible creditable challengers, and build your Imperial Army. Such an Army is immune to the political pressures that cause conventional armies to have to go home because it is a mercenary army. Such armies have been very successful in the past. The Roman Army 2nd Century AD - 3rd Century AD was such an Army and it was extremely successful. If the US Military had used Roman methods to conquer Iraq, there would not have been a 10 year counterinsurgency campaign. For that matter, if it had used World War II methods, the problem would have been solved much sooner.
I offer this to you... would the Sunnis have been able to believe that they had been tricked into defeat if 100 B52s had carpet bombed Baghdad into rubble (think Tokyo raids), and the US Military had been liberal in its use of napalm and carpet bombing in the march north? Would there had been a 1st or 2nd battle of Fallujah if World War II tactics had been used? As it was, US military casualties were light even when the US military was fighting with the gloves on. Consider how quickly resistance would have been effectively demolished in the initial invasion if harsher methods had been used to wipe out the resistance. Or for that matter, the US had gone in with 9 divisions instead of 3 (which was possible with the forces available to the US Army at that time.. it would have taken longer in preparation but the forces were there. Spearhead would be the same, just use NG brigades to hold the line of communications and occupy key points)
By the way, although the US imports some oil from the Mideast, most of the US oil supply is from the Western Hemisphere or Nigeria. The primary customer for Mideast oil is Europe, Japan, China, and India.
Once again, you do not have to occupy the world to conquer it. You simply have to eliminate any possible challenger, force the remaining nations to toe the line by military blackmail (and if the Americans crush the Europeans and East Asians, do you really think that the rest of the world is going to refuse American demands in the face of possible national extinction?)
Krull, your objections are valid... Australia is important because it had become the primary source of raw materials for East Asia.. specifically for China and Japan, and control of it means you cripple their industry without having to literally destroy it. It is also easy to control as the population is concentrated in only a few scattered cities, and the potential as a vast base is pretty obvious. It also gives America (Now, much less in the situation laid out) firm bases for space tracking, and launch sites for southern hemisphere and south polar orbits.
Note that the US is capable of building a much larger ABM system then is currently deployed. Yes, such a move would scare the piss out of the Russians and Chinese... but the Russians are not at this time technologically or monetarily able to match any American arms build up, while the Chinese aren't there yet either in terms of technology. The only nations that could...potentially...are Japan and some of the Europeans, and one thing that the Americans have that the Japanese and Europeans do not have is thousands of spare nuclear warheads sitting in storage and the infrastructure to build more. It takes years to build that, and certainly an evil American empire would get its forces ready first.
Finally Krull, as I pointed out, the whole thing is indeed impossible politically or morally for the United States to do as currently governed or organized. It would take some catastrophe to change our system or provide the will for such as change. But the question I am attempting to answer is whether or not North America has the raw power to do so and I think it does.
The Volunteer US Army peaked in 1987 at 18 regular divisions, plus 3 Marine divisions, plus about 30 Reserve and National Guard Divisions (including separate brigades that could have been organized into divisions). The peak US Army in the Cold War had a few more divisions above this number (once again if you count 3 brigades as a division for this purpose.. there were a fair number of separate brigades). The peak World War II US Army numbered 89 Divisions, plus 6 Marine Divisions with a population of about half of the current USA. It took 3 years to get that number, but it was done. A similar massive increase in the Navy and Air Forces also occurred. Note in World War II only 1 American division was ever permanently eliminated (the Phillippine Division), while several were badly mauled (mostly during the Battle of the Bulge), all were rebuilt before the end of fighting in Germany. In spite of the fact that Russia and Germany built hundreds of divisions, a very large percentage of these were eliminated, and the bulk of both of those nations had half the firepower of a US Infantry Division (which was essentially fully motorized at will).
So in effect, the US is capable of generating probably 200 fully mechanized divisions (including airborne and marine), along with the vast support needed to support such a force. It would take years, but it is possible.
In terms of raw power, the US can generate a vast amount, and only Russia and China could ever come close to that. Which is why you destroy their electronics industry with EMP, their nuclear, air and naval forces with nuclear strikes, and do the same with their shipyards. By the time they recover, it is too late.
Sure, there are details that would have to be resolved (the timing of a nuclear strike to reduce or preclude effective retaliation was a problem the Soviets never solved) but on several occasions during the Cold War era the US could have launched a preemptive strike and utterly destroyed the Chinese and Soviet capability to retaliate to any effective degree (in terms of reducing the ability of the US to carry through what I am suggesting is possible).
I am not saying that America conquering the world is easy, cheap, or even quick.. but it is possible from a strictly economic and military analysis.