For historical and geopolitical reasons some, usually small, islands have great strategic value, especially as they can provide an airstrip, storage and shelter. Diego Garcia comes to mind, a UK dependency minus its people is a significant base for the USA. Other islands in the Indian Ocean are of value, Maisrah (Oman) for example, whilst Socotra (Yemen) oddly has almost none, largely as it has little potable water and the terrain is harsh.

The UK has a number of such assets, an imperial legacy, although some have seen a 'small war' e.g. EOKA's campaign in Cyprus, or a significant international conflict, the Falkland Islands war in 1982.

Non-western nations also have recognised their value, China (PRC) has long been suspected of having a strategy to acquire facilities - a 'String of Pearls':

So I read this Lowy Institute blog article with interest, not for the possible use by the USA of the Cocos Islands, close to Sumatra (Australia), but the reference to use of the Andaman Islands (India):

There are several threads on islands, great power rivalry and the US pivot to the Asia-Pacific.