>>18285913
Unlikely to prosper since the US was not yet strong enough to project power beyond the Caribbean. That only changed after the Great White Fleet and the Spanish-American War.

>>18286816
What if during the Spanish-American War, USA chose to get Cartagena, how much Europe would have change?
Would all Spain have been conquered?

Would have been unworkable and put the US into an essentially permanent adversarial footing with Spain. The US's foreign policy was to turn former enemies into trading partners. Taking colonies away from an imperial power was one thing, but taking away a historical city on their mainland? Wars were literally fought over stuff like this in Europe for thousands of years. It would sour relations with Spain pretty much irrecoverably and worse would yet would inevitably draw the US into continental European politics.

The two founding principles of US foreign policy at the time were "avoid entangling alliances" and "promote unrestricted trade". The US was confident in its growing industrial economy and vast resources, so that if it could trade peacefully with somebody, the mutual prosperity that trade brought would naturally build friendly relations without the need for formal alliances. It left the US free to associate with whomever they wanted and to act in its own self interest without being hampered by binding agreements.

Relations with Spain aside, the US would be responsible for protecting Cartegena in the event another European war broke out (when, not if) which was just something nobody in the US wanted to even countenance.