For every proposed solution, there seems to be a ton of unforeseen problems. I think that the reason they world pull CO2 from the water is that it would be easier to extract large quantities, as the concentration in air is actually very small, volume wise.

Have you ever heard of seastedding? It seems like it could be a way to use this solar energy directly instead of needing to convert it to a fuel. Just have people live on these islands. Underwater farming is also a very promising thing, so all their food needs could likely be meet if they had the right infrastructure.