(Because: http://en.wikipedia.org/wiki/Cane_toads_in_Australia . These are complex, poorly understood systems, and the results will almost certainly not be what you expected. This isn't engineering.)
Done over a large enough area, it can change more than just the CO2 levels in the atmosphere.
Iron sulfate does indeed lack reproductive capability. But it attracts plankton, which is a wide category of organism - some plankton can reproduce.
It's a false dichotomy. There's probably a wide range of things we can do, and picking an option just because it happens to be there & feasible, regardless of evidence of merit, doesn't seem like a winning strategy.
Put another way, you could cut off your hand to treat an infected wound. It's "feasible." But is it anything remotely approaching the best way? Furthermore, what if it turns out that artificially seeding the ocean with plankton is approximately as disastrous for the health of the ocean?
If there are demonstrable benefits, then "do the benefits outweigh the risks" is something that we must consider. To categorically strike out broad classes of solutions because something might go wrong, without even considering the severity of the possibility, is to advocate inaction.
Any solution to this particular problem is met with this nonsensical "something non-descript might go wrong, so we better sit on our asses instead" mentality. What we should be asking ourselves is "What solution has both the greatest good/bad ratio, and can be scaled enough to actually solve the problem". Things are going to go wrong; to stop exploring a possibility as soon as we learn that something could go wrong is naive and if universalized will lead to our downfall.
But that's just it: we have no way to answer that question. We can't say if it's a good idea because we don't even know if it's even going to yield good results, let alone what cost those good results come at.
I agree that we won't hit on some perfect solution which has no trade-off. But making a decision without even knowing what trade-off you're making could actually make things worse! Imagine if this does approximately nothing substantial for climate change, yet it kills off a ton of species. Now we're on a planet with an destabilizing climate and a substantially more destabilized ecosystem.
High stakes cut both ways. You can win big by doing something bold just as you can lose even bigger or sooner. And having people unilaterally try out their pet theories seems like a recipe for disaster. They'll likely be long dead before the effects of their actions are realized anyway.
The attribute of non-replication doesn't equate to "safe for the environment".