To work as a carbon capture mechanic, iron fertilization-driven algae blooms would have to die and sink to the bottom of the ocean, thus locking up their carbon in oceanic rock.

The concern is they would die and float, releasing all that carbon back into the atmosphere via decomposition gases. Then we would have all the effort of the fertilization, all the ecosystem disruption of the algae bloom, and maybe negative benefit as far as carbon since the ecosystem disruption could mess up carbon sinks that were actually working.