This assumes that global warming is the problem, but arguably the most pressing aspect of carbon pollution is the acidification of the oceans which this plan would not address. It might make more sense to focus on capturing carbon pollution than to mitigate some of the side effects of rampant carbon pollution.
I'm not sure I buy that, but sure, both are important problems. Question, what do we know about the ocean as a carbon sink? Is it's capture rate variable with anthing? Is it easier to capture carbon from the ocean than in the air? Could we try to increase the capture rate into the ocean and then extract rapidly from the same area?
Someone else pointed out that we can cause blooms. That's basically what you want, because plankton or algae sequester it. I don't know that we can "hack" that without risking damaging the oceans though. They're pretty good at what they do as is.
It is a gas exchange though, so heat and pressure have an impact. They're not great for marine life though. Surface area does as well, though it'd be hard to meaningfully change the ocean's surface area.
The bigger issue would be containment. The ocean is huge, and a very good CO2 sink. Anything that's going to make a significant dent in the total CO2 absorption of the ocean is going to have to happen over a very large area. Things aren't going to be much better if we sterilize the ocean in the process.