Controlling a territory has been done many times with a very small force. The key is set up a hierarchy and have locals do the door-to-door ground work. Flying in the imperial marines to patrol every village street in backcountry Afghanistan is completely insane.

Historically, the way to control a territory is as follows: you go to each region and you find the local strongman with the best combination of reliability and strength available. You say: "We will support your control of this region, if you provide security and support our imperial policies [those policies could be anything, depending on the desires of the imperialist. It could be providing natural resources, converting people to a certain religion or even spreading woman's rights]. If you support our policies, you will otherwise have freedom to rule according to local custom. We will provide you money and resources. If you fail to support our policies, we will violently remove you."

Under such a policy, you do not need hundreds of thousands of imperial soldiers patrolling the lands, you just need enough soldiers to remove any local warlords that get out of line.

This raises the question: why hasn't the U.S. done the above? My theory is that the U.S. leadership are actually True Believers in democracy. The above method of rule makes it impossible to spread democracy, because the occupying power must choose the strongman - the locals cannot choose the leader via elections. Since the U.S. wishes to spread democracy, it cannot use this method of rule. Furthermore, such overt imperialism contradicts the U.S.'s founding myth as being born out of resistance to imperialism. Few states can overtly contradict their founding myths. So instead, the U.S. has chosen to maintain security with its own forces, so that the locals can have elections and choose local leaders, as part of a transition to democracy.