An alternative POD would have Heligoland as a British mandate after WW1.
I agree with you on this though. I think the Germans would have taken it in the First World War, unless Britain seriously fortified it.
Through the Thirties, it would have become a magnet for dissidents, and almost certainly you would have seen Brecht head there, for example (much as Victor Hugo fled to Jersey to escape Napoleon III).
And when the Second World War started- well, being able to bomb Germany (especially Hamburg) on the 3rd September 1939 would have been an incredible advantage, and might well have been able to be used to start an earlier campaign against German industry and railways, slowing down German mobilisation against France, Belgium and Holland.
Maybe even the surviving aircraft of the Danish military could have escaped there.