In addition to capturing carbon, forests (of native tree species) provide many ecosystem services, including fresh water retention in the land, food and habitat

In addition to capturing carbon, forests (of native tree species) provide many ecosystem services, including fresh water retention in the land, food and habitat for other species, shading of the ground, etc that a greenhouse full of algae would be challenged to provide. Most of the carbon stored in a forest is subterranean and increases significantly over time.