When you are the most powerful and most feared country in the world with a military that is so far superior, so far advanced, so entirely complete, as compared to any other country, than there are a multitude of ways to conduct your military business. While there is a lot to be said about simply facing your enemies and doing battle, there are other alternative ways which will cost both sides less in military personnel, civilian casualties, and military armaments. A siege is a type of warfare that should be employed as often as it is available. A siege properly conducted will save significant lives on both ends and is probably more humane than virtually any other alternative.
Because modern military units need access to shelter, food, and energy, taking away or impacting the enemy's access to any of these will significantly weaken them. The type of engineering and forward thinking needed to perform these actions is well within the capability of a country like the United States which prides itself on assembling thorough and complete information. While there are legal protocols in regards to what actions are or are not allowed in regards to siege warfare and the treatment of civilian populations, none of them are game stoppers. The object of any siege is to vanquish the enemy by putting them into the unenviable position in which although their defensive position may be strong, they are not strong enough to attack and further they do not have the means to self-sustain themselves over an extended period of time.
Performing a naval blockade is extremely effective in tightening the grip on recalcitrant countries. On land, access to roads can be stymied, communications disrupted, and the like. The objective is to get the defender to surrender without having to actually go to battle. Siege warfare may be slow but it is also steadily effective, like a snake applying constriction. Sometimes the enemy is reluctant to recognize the futility of their situation, but an unrelenting reality will often bring clarity.
Siege warfare can also be analogous to hostage negotiations, in which you have a significant risk that innocent civilians will be hurt or killed if the paramilitary unit or equivalent was to go in with full force in which they will be trying to simultaneously protect the hostages while also taking out the bad guys. Sometimes that is the only choice that can be made but that choice often comes with unfortunate collateral damage.
When you are in the superior position, most of time there isn't any real pressure on you that something has to be done, right then, right there. Take away easy access to items that humans need to survive on and capitulation will come. History has shown again and again that when the opposition loses their ability to sustain themselves, they will eventually submit. Anytime that you can get the enemy to walk away from their entrenchments and to surrender their arms without having to do battle with them, you have succeeded in your primary mission which is to neutralize the enemy without unnecessarily endangering your forces or civilians.