The problem with this line of reasoning is that it has been, and is until very recently this very 'umbrella' that the US wishes to spread around the world, as she sees it as advantageous.

Post WW2, both the German and Japanese military were greatly limited, or outright abolished.

The numerous bases of the US around the globe in any country and climate imaginable are not only selfless bastions of people in need - they serve very concrete functions, namely protecting trade routes and political stability in systems that are beneficial to the economy of the US.