It seems to me that forming a federation or even becoming a single state would be greatly beneficial in terms of GDP, security, resource sharing, and influence.
This is a bit like asking "Why don't Canada and America become one state? It would benefit both of them!"
They exist for the same reasons that any other nation exists. You have areas of land populated by people with fairly homogeneous backgrounds (language, religion, culture, ethnicity, economics, history, etc.). There's enough similarity in the populations of these islands that they feel a national bond to the other people residing on their island. However there's not necessarily a shared bond with other island nations, and therefore each one prefers to maintain its sovereignty.
It's also important to note that some islands HAVE joined together to form a bigger nation. The Philippines and Malaysia are great examples. The Philippines has about two thousand populated islands, while Indonesia has almost a thousand populated islands (additionally they both have thousands of more unpopulated islands), and all of those islands are under one flag.