Most quick-growing plants have a short life-cycle after which they decay and put their carbon back into the atmosphere. The only plants that really lock up carbon for decades or centuries are trees, and growing new forests is slow and daunting. You can solve the fast-growing plant problem by continuously growing plants (so as the old ones die, new ones lock up the same amount of carbon), but that means that a given acre of land has to be devoted in perpetuity to locking up X amount of carbon. And fast-growing, large plants tend to degrade soil quality -- they need rich nutrients to support that fast growth. They also need water, which is not necessarily locally abundant.
Reforestation is still probably the best way to capture carbon from the atmosphere. Do something where you build a young-growth forest, cut down trees and do something with the wood other than allow it to decay or burn it, let new trees grow. But it's not just a matter of flinging some seeds on the ground and yelling "Done!"