I think you misunderstood what the parent was trying to say. The poster is suggesting we replicate one of nature's lesser carbon sequestration methods, which is the burying of plant and animal matter that will eventually be transformed into oil. The parent is suggesting that as soon as a tree matures and slows down its growth, we remove it, bury it, and replace it with a young tree that will pull carbon out of the atmosphere faster.
1) You are correct that such a method is a timber farm and that a normal ecosystem will not exist. But since the goal of the forest is not to provide usable tree products, the need for pesticides in not present. If a disease runs through and wipes out a large number of the trees, we simply bury those trees earlier than we wanted and start growing new ones.
2) If you think that managed forests in developed countries are still often clear-cut, you know very little about the timber industry as they have been selectively cutting trees since the eighties.
3) This plan would not put a pressure on landfills because it would require a specialized location anyway. To get around the methane problem, this area would have to be far deeper than an above ground landfill. In fact, it may be easier to turn the trees into woodchips and fill up abandoned mines with them. Or perhaps produce a wood-pulp slurry and inject it back into former oil-fields.
