There's got to be something that grows faster, and is easier to sequestrate, than trees. Bamboo, maybe? Seaweed? Algae? Dry it off in salt pans and dump it in the deep, cold ocean?
That's just dumping more carbon into one of our natural sinks, I think, rather than trying to create a new artificial sink. Even just using it as fertilizer has got to be an improvement over using inorganic fertilizers.
Cool idea, I'd never heard of this. TL-DR is that there are huge portions of the ocean that are nutrient-rich but have little life, and one hypothesis is that iron is the limiting factor here. Since various phytoplankton need iron to survive, why not dump iron in these places, watch the phytoplankton now thrive, and enjoy their carbon sequestration?
The answer seems to be "well, we don't really know what the effect would be". Some algae blooms are not good (red tide), deliberately altering an ecosystem is generally dangerous, it's not clear whether the positive local effect on carbon has some side effect elsewhere (maybe we're just moving phytoplankton around the ocean). Even doing experiments on this is difficult (the world's oceans are weirdly regulated), and current financial incentives don't make it all that enticing either.
That's just dumping more carbon into one of our natural sinks, I think, rather than trying to create a new artificial sink. Even just using it as fertilizer has got to be an improvement over using inorganic fertilizers.