WI: US keeps Tristan da Cuhna Islands?

The Tristan da Cuhna islands is a small archipelago located in the South Atlantic, on record as the most remotely inhabited place on Earth. No humans permanently lived on it until 1811, when american whaler named Johnathan Lambert settled it with three other people and re. Not much else happened until when British annexed it during the War of 1812, where it remains a British Overseas Territory to this day.

But what if the US for some reason or another decided to invest heavier on these islands for one reason or another and got to keep it? How would this affect US navy and foreign history for instance?
 
The Tristan da Cuhna islands is a small archipelago located in the South Atlantic, on record as the most remotely inhabited place on Earth. No humans permanently lived on it until 1811, when american whaler named Johnathan Lambert settled it with three other people and re. Not much else happened until when British annexed it during the War of 1812, where it remains a British Overseas Territory to this day.

But what if the US for some reason or another decided to invest heavier on these islands for one reason or another and got to keep it? How would this affect US navy and foreign history for instance?
Not much? just keeping a few extra ships to send supplies but nothing? could become a state or what?
 
could become a state or what?
Probably could just remain as a territory, one that's the butt of the joke in US (and by extension) culture as a sad group of islands where nothing happens. On the other hand, the US would probably use this as a fishing/whaling outpost, which while seemingly minor could have ecological butterflies over time.
 
Probably could just remain as a territory, one that's the butt of the joke in US (and by extension) culture as a sad group of islands where nothing happens. On the other hand, the US would probably use this as a fishing/whaling outpost, which while seemingly minor could have ecological butterflies over time.
But that much? still State or bust....if not why even get the islands?
 
Turn the whole place into a super-Alcatraz and/or research facility and add rumors/legends as desired?
 
The fact that there is not even a airport / landing strip speaks volumes on the strategic unimportance of these islands. If they were of any modern value it would have become self evident either during the height of the Cold War or during the War on Terror as a redition or black ops location.
 
Maybe a remote training location or space launch tracking station later makes them slightly larger? A great place for a large naval base in a Cold War where superpowers are trying not to look as imperialistic?
 
The most this would ever be would be a territory. This island would never support a population sufficient to qualify for a state. If Puerto zrico was ever made a state, theoretically Tritan could be attached to that but on its own never qualify.
 
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