I always laugh when people suggest these meek tiny European states should be in charge of running the world and how much more civilized they are. The reality is that these countries aren't meek by choice and we already know from history what a country like Belgium would do if given a tiny sliver of power.
America is a federation of 50 states. The EU is trying to become a federation of the European states.
Belgian atrocities in the Congo suggests that would be a very, very poor choice
I think the problems are far easier to explain. Watching the documentary Restrepo, I was surprised to see how terrifyingly stupid American GIs are at anything but actual warfare.
The most telling scene was a meeting they had with the local "elders". This was in one of the most isolated valleys, even by Afghani standards. They were talking about a road to be build, and promising jobs for the locals.
Yet it was absolutely clear that these villagers did not even share the concept of a "job". They were goat herders mostly, and possibly some farmers. I'd bet that not one of them is a wage-earning employee or worker. They simply tend to their family's animals.
"Trade" is probably understood in these places, "jobs" is not. They tried to win over the local population with promises entirely based on an American POV.
In larger cities, such promises might have had a better chance to succeed. But I think it's instructive to look at the only people whose "hearts & minds^ the US actually managed to win: translators and other local employees tend to be the US' most ardent supporters. That's maybe due to the money they got, yes. And there's some selection bias at play, as well. But if I had to guess, I'd say simple, honest day-to-day social contact had the most influence.
I think the Us military should form a brigade entirely made up of hippies that can play instruments, like to talk to strangers, can play soccer and basketball, grow weed, and are good petting dogs and getting children to smile.
More seriously: the US has nuclear weapons, rendering them safe from any direct confrontation with enemies challenging them technologically.
They have a conventional military 10x the size needed for the sort of intervention that actually succeeded in the past (the Balkans, the first Gulf war). The rather unsuccessful wars (Afghanistan, Iraq) were lost not for technological reasons or any other dimension of military might, but because the US military sucks at convincing people of the benefits of democracy.
Want to win the next ten wars? Put the money into Hollywood blockbusters and the world's best Halal fast food chain.