The reasons that the Americans fought along with Colombians, Ethiopians, and Puerto Ricans, were mostly geostartegic, economic, and territorial.
They fought along with the Colombians because Colombia has an excellent geostrategic position in the continent that is not very fond of the US. So by having an ally in Colombia they were able to have much better control and to be in a much better position on the affairs in South America.
Ethiopia was a zone of interest because it is crucial as a military base that will be close to the Middle East, so having an ally in them was allowing them to build their military facilities.
Puerto Rico was a territorial zone of interest, and the US wanted to keep it under its own governing because an independent country of Puerto Rico might have gone in any direction really, and even become an ally with some of the American arch enemies, and thus becoming the ''second Cuba''.
