[...] And how about whenever there's some natural disaster in the world, like say the Bandah Aceh earthquake, within days you have a U.S. carrier parked off the coast and flying in life-saving supplies. [...]
Fair point.
But the thing with this kind of arguments ("the world owes us because
without...") is that you have nothing to compare it too: there's only one reality. Everything becomes speculation and there might even be valid arguments to claim the world would be better of without the US. And it's very easy to find arguments to say someone owes someone else.
Look at a night satellite photo of North and South Korea and the contrast. Who do the South Koreans need to thank for that but the United States (along with our allies in that conflct)?
Well, without the arms and space race with the USSR it's not even sure we could enjoy that night satellite photo at all. So maybe the US owes the Russians for that?
Without Japan attacking Pearl Harbor it's not sure the US would have joined WW 2. Possibly not leading to an arms and space race. Maybe the US owes Japan?
Without the expertise of captured German scientists and European emigrants the outcome of this arms and space race could have been different. So maybe the US owes Nazi Germany?
Compare it with another argument: "if you could travel in time would you kill Hitler?". People would say yes because the world would be better without this evil, right? You could save millions of lives from the Holocaust or battlefield if you did. But the technical advancement during WW 2 in chemistry and other areas also led to a better farming industry after the war, saving billions of lives who would most certainly have died otherwise. Hitler is a shit stain on our timeline, but without WW 2 it certainly would not have been a better world. So, do we owe Hitler?
[...] We're under no obligation to do any of that. [...]
Is it? Then why should the US be better the the rest and why should we be thankful?