The #1 concern is that this is borrowing from Peter to pay Paul, that is you end up depleting nutrients other than iron so that there is less production somewhere else.
A #2 issue is that it's not as simple as it sounds, you can't just dump iron off the size of a barge and expect it to work, you really need to be monitoring the process and need a whole flotilla to do that.
Another issue I think would be putting this reflector anywhere other than where the polar ice caps exist could potentially change current temperatures and further mess up the global climate long term. Unintended consequences.
One unintended consequence of iron fertilization could be the promotion of growth of toxic plankton that add neurotoxins to the food chain (e.g. “Red Tide”) but that’s not the only one.
Another interesting aspect of this is that the UN Law of Sea forbids this. Most countries with a coastline are signatories with the notable exception of the US:
https://en.wikipedia.org/wiki/List_of_parties_to_the_United_...
Notably if you were trying to do this, most countries, like Japan or Australia, could refuse the use of their ports.
https://groups.google.com/g/CarbonDioxideRemoval/c/gslzzNXya...
Every time this has been brought up since the 1990s, it has driven scientists over the edge. As I pointed out to the CDR group, this is just one more case where the Algorithmic Information Criterion is ignored as a resolution to scientific controversies (rendered intractable more because of their very importance than the lack of data).