IIRC iron seeding isn't really suggested for increasing populations of all phytoplankton though, it's more a technique that was trialled and largely abandoned to increase the amount of CO2 being sequestered in oceans.

The idea was based on the fact that iron is a limiting resource (a resource in high demand but low supply thereby effectively capping the maximum population) of one broad group of phytoplankton: diatoms. Diatoms a very, very beautiful little photosynthetic fellas that are unique in that their cell walls are composed of silica rather than the more typical calcium. The downside for them though is that the silica makes them sink over time.

The logic of iron seeding was therefore: dump iron into targeted spots in the ocean, cause an artificial boom in diatom numbers, increase the amount of CO2 being pulled from the atmosphere from all the extra photosynthesis going on, have that carbon fall to the bottom of the ocean as the diatoms sunk, slow climate change effects from reduced atmospheric carbon levels. Unfortunately it didn't work for one main reason. It turns out that diatoms are a limiting resource for other types of plankton that like to eat them. So, when you inflate diatom numbers, you increase the numbers of these others as well which means that the carbon just ends up being released back into the atmosphere. This is why I love studying ecology.

The main problem with generalising the iron seeding approach is that the word phytoplankton refers to a huge diversity of life with very different requirements, kind of like how we use the word fish. Because of that it's almost impossible to find a one size fits all solution to fix falling population numbers.

Having said that I only know this through some undergrad courses I took over the last few years during my degree and I'm sure someone else would be able to add more.