Probably has something to do with the fact that desalinization plants are ridiculously expensive when you live on the same land mass as the factories that are building all the parts for them, and the price rises dramatically when it all has to be loaded up onto container ships, transported to you, and then built by a foreign company, and most of those island nations are incredibly broke.
The problem with desalination is that it's expensive and you can't dump the salt anywhere. It creates a brine that kills fish. That would hurt the environment and the tourism industry.
Not only that, they get a ton of rain every year. They're tropical islands. There's enough water, they just need to collect it. Desalination is a technical solution when they really just need boring infrastructure.
This has a lot more to do with consumption than with production. Most of these islands are small, and it's unrealistic for them to have large populations or a heavy tourist industry without desalination plants. Energy needs to become cheap, and honestly, wind farms and solar can help with this.