Well, we already have the plants, and they are obviously not getting the job done. We likely don't have enough land that can grow them, and it might even be dangerous to create some kind of super-plant and stick it into the sea without knowing the environmental impact of doing so - what if it overmultiplies and not only clogs the seas to make shipping impossible, but sucks virtually all the CO2 out of the atmosphere and plunges the planet into an ice ball. I once read of an alien attack that was accomplished entirely by tricking our scientists into creating some single-cell critters that they carelessly allowed into the environment, they found their ways to the sea, and commence to sucking all the oxygen out of the atmosphere, suffocating all animal life on the planet. Forget how the planet was saved, but it was probably unworkable and the planet would actually have been destroyed.
Doing our geo-engineering without summoning the fire of using living things to do it might be a safer route. If we make a machine that is detrimental to our survival, we can turn it off. Living things in the biosphere are much harder to control.