Algae itself needs a functioning ecosystem to survive, to much algea will cause it to kill itself due to overpopulation (e.g. using up resources and dead algea not being cleaned up) while in a small scale humans can care for the algea, taking the place of the ecosystem, for any large area this would be unfeasible and the ecosystem including the algea would collapse.

A benifit of biodiversity is greater resilance to change, by selecting for the growth of specific algea using iron you cause other algea/plant that rely on the prior ecosys to die out (including those reliant on other organisms which died). this group of less diverse algea will be more susceptible to change, (diseases or environmental change) and as most of the algea in the world will be similar, most of the algea in the world could get wiped out in one go.

So the likely outcome would be an initial spike in carbon capture before the environment becomes unsuitable, collapses, and most of the algea dies.

So all im all at any meaningful scale in the sea this is and will always be, a terrible idea.

(A better idea would be lots of small manigable algea tanks which could realistically be maintained and won't affect the current diversity, diseases could also not spread between them. This would be expensive but could actually work as a long term solution)