Not the largest
Given that US military is larger than the next 6 largest armies combined
This is not true. The United States military is more expensive than the next six most expensive militaries. The US army is not even the largest, much less bigger than the six largest not counting the US.
According to World Atlas, the US has the second largest military in the world. It's well behind China and a bit ahead of India and North Korea. A bit more research suggests that this is active military personnel.
According to Wikipedia, which bases its numbers on The Military Balance from the International Institute for Strategic Studies, the US has the seventh largest total military, including active, reserve, and paramilitary personnel.
More expensive per capita
The United States spends more per soldier. Some of this is better gear, but some of it is simple costs. The United States has a comparatively high cost of living when set against countries with larger populations. In particular, India is less than a third the cost of living as the United States. And China is a bit over half.
The US is twentieth (according to the World Bank) in percentage of GDP spent on the military. This is behind, for example, Russia.
Twice during the twentieth century, Germany was one of the main belligerents in a World War. After the second one, the allies, including the United States, banded together to keep it from forming a new army. To this day, the US has military bases in Germany.
For similar reasons, the US has maintained a military presence in Japan, which continues to this day.
The US participated in a civil war in Korea and maintains a military presence in South Korea to this day.
The US, which has one of the two largest Jewish populations of any country, gives military aid to Israel (the other top two country). This also may explain some of its participation in other conflicts in the Middle East.
The US was at war for the entire Obama presidency. This was the first time that a president served a full two terms while at war.
The US has the third largest population of any country, and the highest cost of living of the nine largest population countries.
It's also worth noting that war is expensive. The US has not fought a large scale war against a comparable opponent since the Cold War. In an actual war with another country, the US military budget would likely increase. Defense spending in World War II passed 40% of GDP, more than ten times what the US spends now.
Some of the comments suggest that I'm arguing that the US is not the most powerful military in the world. I'm not. What I'm pointing out is that the US is not more powerful militarily than the next six most powerful militaries. In particular, the Chinese and Russian militaries are, combined, probably more powerful than the US military. And certainly if you mixed in three of the NATO countries besides the US, those five countries would be more powerful militarily than the US.
The correct statistic by which the US beats the next six countries combined is expense. The United States has the most expensive military in the world by a large margin. Just a few years ago, it was actually more expensive than all the rest of the world's militaries. However, as I noted, this does not actually mean that it is six times more powerful any more than North Korea's size means that it is twice as powerful. Neither size nor expense are good proxies for military power.
I've ignored that you used the word "army" rather than military, even though that makes this worse. Most of the expense of the US military is in things like the Air Force and Navy rather than the Army per se. I've been assuming that you meant military.
Both the US and Russia have sufficient nuclear weapons to end civilization as we know it. Other countries may as well. So put aside any significant use of nuclear weapons, as a country that makes major use of nuclear weapons will lose any conflict (along with every other country).
Quality vs. quantity
Quality does not always beat quantity. Take the US Civil War for an example. The South had the higher quality army. Most of the officers were from the South. They pretty consistently took fewer casualties than the North did. Yet the North won in the end.
This isn't to say that North Korea would be able to outlast the US in a war. The US has more capacity to increase its army than North Korea does. But it might mean that China could outlast the US. Or maybe not.
In actual, non-nuclear war two militaries that are evenly matched make for the worst war. Because both sides are close to parity, neither will win quickly. The longer a war lasts, the more damage it does to both sides. So militaries would prefer to engage when clearly more powerful than their opponents. Often more resources will reduce the long term cost of the conflict.
What could the US buy with a higher defense budget than it has now?
This may be the question that people find interesting. I didn't really get into this in my original answer, as it seems obvious once one realizes that the US is not that far ahead of other countries. But if you want some specific examples of things that are not include in the current US budget, consider
Updated nuclear missiles. The US has been decreasing the size of its nuclear arsenal since the 1980s. Some believe that the current arsenal might be getting to the point where it will start failing. They want to replace missiles that are forty or more years old with newer, more reliable missiles.
More updated planes. Many of the US planes were bought decades ago. During the last election, pictures were posted of planes with no engines, etc. It's not clear that this isn't purely business as usual (once planes are no longer built, it makes sense to dismantle some to fix others), but some have called for an increase in new planes that don't have to be repaired immediately.
Two front war. In 2008, the US was participating in wars in both Afghanistan and Iraq. In 2016, the US could not have actively done so. It would have had to choose between the two countries. The provisional plans called for fighting a holding action in one theater while actively trying to win in the other.
This may not seem that important, but it matches actual experience. It is relatively common for the US to be involved in two fronts. Not just the recent Afghanistan/Iraq example, but World War II's Pacific and Atlantic theaters. Or the Civil War, where there was a Mississippi theater and a Virginia theater. And of course the risk that a country might be more willing to act if the US was already at war, knowing the US couldn't fight another war at the same time.
More volunteers. The US could pay more on recruiting and wages. During the Iraq war, the US called up not just the Reserves but the National Guard. Swapping out more people who don't want to be active military with people who do would improve morale.
Increasing the number of reservists would also help. They provide a trained base if ever the draft were reinstituted to fight a large scale conflict.
More tanks. Russia and China have more tanks than the US (source). Of course, tanks have not been that useful in recent conflicts. Most vehicles are used to move infantry rather than to fight themselves. But this is an area where the US actually lags.
Better logistics. I've spoken with veterans who had trouble getting supplied with food while in Iraq. I doubt this was widespread, but it was a problem. More money spent on supplies and getting supplies to where they are needed could be helpful in future conflicts.
Better armor. Many military vehicles capable of operating in Afghanistan (rough, mountainous terrain) weren't armored, leaving them vulnerable to improvised explosive devices (IEDs). This lead to the Donald Rumsfeld quote: "As you know, you go to war with the army you have, not the army you might want or wish to have at a later time." Some would prefer to equip the army with what they wish it would have.