alt Hacker Newsit actually is a bad idea if you look into the details
trees aren't just carbon, they are bio mass/nutrition
and if you constantly remove bio mass you sooner or later run into issues
(Which we already do in some places, e.g. when over using fields (see US dust storms), or with some managed Forrest getting increasingly more unstable not just because of warmed climate but also because of removing dead treas leading to an interruption of the natural nutrient recycling (and insect habitats) leading to Nutrition deficiency in the long run.)
but we do have working carbon removal technologies, they are just not cheap
hence why you want companies to pay for them, it gives them a huge reason to reduce emissions instead
The point of turning the trees into Charcoal is to return all the non-carbon elements to the environment and remove any metabolic activity from releasing that carbon.
The USA currently produces about 70 million tons of paper per year, which is about half carbon by weight. We produce about 2 gigatons of lumber per year, which is again about half carbon, all absorbed from the atmosphere.
Unfortunately, we produce like 40 gigatons of CO2 per year. So we would have to scale lumber work dramatically. It's also not a clean industry itself, reliant on heavy machinery running on gasoline or diesel, and turning that wood into charcoal would require massive refineries.
IMO more effective bets are figuring out how to artificially induce massive blooms of algae and plankton in parts of the ocean to essentially recreate the conditions that lead to the hydrocarbon deposits in the first place. There's some work on this right now, but like any massive engineering and ecological tampering, there will be tradeoffs and downsides. I also don't know how you prevent the dead plant matter from decomposing and releasing the carbon.