Oops!
I was defending the honor of Frederick Franks, who led 7th Corps in the Gulf War. He was often criticized for not killing enough of the Republican Guard during the Gulf War, under Bush the First. I mistook Tommy Franks for him - a whole other General Franks. Fred Franks kicked ass!
I’m also just a keyboard jockey doing this analysis for fun, but I give Bush a lot of credit for biting off a difficult and dangerous task, and have been impressed by his character in respecting and caring for those who served. As Teddy Roosevelt was fond of saying, credit belongs to man in the arena.
In 2003, we were heroes to many Shia in Iraq, after removing the brutal persecutor Saddam - a Hitler-like monster. Even Iran, as “Death to America” happy as they were, took some time before starting to agitate against the US within the Iraqi Shia population, so powerful was the popular joy over the downfall of Saddam. In 2004, American soldiers could walk around Baghdad individually.
But Iran was immediately at work infiltrating their loyalists into positions of power in the new Government, and preparing to fight in Iraq. Iran had much more to fear from the US than Syria - suddenly surrounded in Afghanistan and Iraq by their “Great Satan” who had openly called them part of the “Axis of Evil” (which they were). The Iranian/Saudi surrogate war entered a new phase when Saddam fell, with the Gulf Arabs still funding their B team terrorists, while Iran stood up its militias within the Shi’ite community.
I believe that dissolving the Iraqi Army was absolutely necessary, because they were totally an organ of the Ba’ath Party (which had twice conquered Iraq through Secret coups). The Ba’ath had extensive plans to retake power. The Army was central to their plans, and was by far the most powerful asset they could use to do it. US occupation forces would have been vulnerable to sudden mass slaughter, if the Iraqi Army had launched a sudden surprise revolt targeting the Americans.
So Iraq was a big undertaking, and Democrats (as well as many Republicans) were actively seeking to limit resources, so Rumsfeld was was selling his better/faster/cheaper concepts to accomplish the mission within the financial constraints from Congress. The bottom line was that no 20 new divisions would be coming from Congress. Of course, we could have done more with more, and at less risk. We had a budget then, and great difficulty in raising spending without raising taxes - it is shockingly different from today’s environment of wanton disregard for math.
From my perspective, Rumsfeld was the big proponent of the lean footprint, and the State Department institutionally desired (as is typical) less military influence or control of the situation. Ultimately, I believe you are right, that a lot more resources would have decisively improved the situation. Congress then exercised the power of the purse.
The conventional approach to reducing the size (and thereby the cost and casualties) of your occupation force, is to install a strongman regime, and let them impose order. We tried to both have a lean occupation force (based on theories that technology and tactics could be force multipliers), and to allow a lot of political freedom. Enemies exploited freedom to organize, and there was a dearth of honest leaders to administer the Government. A more Machiavellian use of the CIA and an imposed Iraqi strongman regime could have made a big difference as well, but with other costs.
As you noted, the Mongols were incredibly efficient in occupation. They did in fact use repeated instances of wholesale genocidal slaughter to enforce their rule. Parts of Afghanistan, like Bamiyan Province, were totally depopulated by the Mongols in retribution for rebellion. To this day, the local Hazara population are descended from the Mongol occupation force.
The buck stopped with Bush. Re the power of the purse, the time to ask for 20 new divisions was in the weeks after 9/11, when his poll ratings were in the 80's, and Congress would have denied him nothing. The "go shopping" thing made him look unserious and the "tax cut" thing made like look like he was engaged in business as usual, using wartime-related political capital to reward the GOP's fat cat backers. He came off looking simultaneously lightweight and hyper-partisan.
Standing up new divisions would have simultaneously given the nation the clear messages that business as usual was out of the question, and that the nation was at war, and sacrifices would be needed. It would also have given him the ability to blanket Afghanistan with troops to corner, trap and demolish the Taliban instead of playing whack-a-mole because of insufficient troop coverage before moving on to Iraq.
The theme that sticks out again and again is the way in which at every critical juncture, he made the wrong decision. The recurrent media theme is "Bush lied", which is flat-out wrong. My problem with Bush is that he was just a lousy decisionmaker. He asked the wrong questions, and made the wrong decisions every step of the way.