The US set up a pretty sweet deal for itself all things considered IOTL: US businesses got free run of Cuba and the American government rather than having to pay the costs of administration and occupation (as a full American presence in Cuba would have required), it had effectively unlimited power to change Cuba's government at any time, and it historically (well, before the Good Neighbor Policy anyway) showed little hesitation to exercise that on any Cuban leader that wasn't malleable enough for American interests. So in a lot of ways, the United States got pretty much all the benefits of having Cuba be firmly in its pocket without actually having to pay the cost of running the place like a colony. The domestic will to get tangled up in that kind of thing in Cuba really wasn't there.
Of course, the public wasn't exactly keen on the kind of direct rule that the US imposed on the Philippines either that subsequently resulted in one of the nastier conflicts the US has ever fought.
That said, this being a time when the masses of Africa and Asia were either completely or in the process of being subsumed by Western colonialism, it probably wouldn't have been impossible under all circumstances for someone in Washington to decide that Cuba is better off under direct rule. Considering that this is a time when colonial powers were fighting wars halfway across the world in India and Sub-Saharan Africa, an American bushwar in Cuba is going to look like small potatoes by comparison.