Trees decomposing and being consumed by other trees is literally how it's worked for untold millions of years, so doesn't seem like a problem to me ...
Forests also provide local cooling, improve the water cycle, and aid biodiversity. A world with forests is a healthier world.
It's also how we got all the carbon in our top soils. A 6 inch or more covering of carbon (mixed with minerals etc) covering huge parts of the earth's surface.
Planting trees, harvesting them, and turning them by pyrolysis into biochar/charcoal and then burying it can partially restore these soils and sequester carbon at the same time.
Oh, absolutely. It would take generations. But taking forestry waste and turning it into a soil amendment is a worthwhile endeavour even from the POV of improving food production.
Forests also provide local cooling, improve the water cycle, and aid biodiversity. A world with forests is a healthier world.