The surface area of a roof is tiny in comparison to planting miles and miles of forest. It's also very weight sensitive, but the goal is to capture, remove, and continuously replace a huge mass of solid carbon. Finally, green roofs select succulents and other plants that grow slowly, but for this goal you want a species that grows like a weed and produces literal tons of biomass that have to be trucked away and be buried.

The "plant trees for charcoal" idea is basically the bio-engineering method of "build huge photovoltaic solar plant, use electric energy to power chemistry to convert CO2 to oil". Photosynthetic plants are pretty efficient, compared to silicon solar cells, and they're (literally) dirt cheap.