If forests did not then some other body of plant mass would have to - erosion and weathering of rocks takes a lot of oxygen out of the atmosphere, and this needs replaced by biology by photosynthesis. In the long term this is the reason the Earth needs to "breathe", and plants are how it has done so. Plants die and are eaten by ranging animals, dispersing their material, creating soils and eventually sediments. This is a long cycle through which carbon is returned to ground, sometimes to metamorphic rock.

It takes place at a lower intensity than our burning of fossil material and forests in recent history. Regrowing forest, usefully captures carbon and releases oxygen more rapidly than mature forest, but of course not rapidly enough to make up for burning them down.