Providing relief during earthquakes and hurricanes is important, but it is not as important as facilitating job creation.
A nation can go through a decade without a single earthquake or serious hurricane damage, but unemployment is a more serious and more constant problem.
If you noticed, most (if not all of these nations) have unemployment problems.
The US won the “soft power” stakes during the Cold War largely because it could provide more economic opportunities than the Soviet bloc. If the US or its allies are no longer seen as the premier catalyst for economic growth in many parts of the World, then US leadership is badly compromised.
Secondly, we are talking about the Caribbean here, America’s backyard. If the US can’t be competitive here, at least team up with India and inject some dynamism in your trade relations. There is no point chasing bad guys half a World away if you neglect your corner of the Globe.
Thirdly, if you were paying attention to the news, you would have noticed that China launched a 10,000 tonne hospital ship in 2008. They are thinking ahead about projecting soft power during earthquakes and hurricanes.
I don't believe this is just about the economy.