It doesn't need to be stored forever. As trees die and are farmed, they are replaced by new ones. Large forests in conjunction with reduced CO2 emission and renewables is the best answer to climate change, not some band-aid to mask the problem.
Land usage is abysmal, and there's a lot of waste. Stop cutting down trees and stop urban sprawl.
As a side effect we might just be able to stop a mass extinction due to loss of habitat.
I agree there's a lot of waste but with the population expected to go up by 3-4 billion in the next decade that urban sprawl is not going to stop, and we're going to need 2x more land for food, especially as we're overfishing our acidified oceans today. Bio capture it's just not feasible because of the land required