My understanding is that the fossil fuels we use for energy were
generated during the Carboniferous period by burying carbon rich plant
matter in anoxic swamps. If we are causing climate change by reversing
this effect, dumping tons of carbon back into the carbon cycle... why
recycle paper, or other products created, necessarily, by pulling
carbon from the atmosphere?
Wouldn't a more beneficial method of disposing of such waste be to
find a method of isolating them from the effects of weathering and
keeping the carbon they contain locked up as long as possible?
I think part of your question has gone unanswered, so I'll give it a shot.
I'm not sure there's enough anoxic bodies of water/swamps available for that kind of project, and 2, it's not easy to bury something in a swamp, there would be issues of transportation (many million tons of recycled paper), so it would be fairly work intensive. It's not easy burying millions of tons under a swamp and paper floats - so, there's no guarantee it would be long term anyway.
Let's look at how much paper is used. Roughly 3.3 billion cubic meters of trees are harvested every year, over half of that goes into fuel for cooking and heating. 17% goes into making paper (presumably that would go up if we stop recycling, so lets say 20%-25%. And wood is about 50% carbon (sources all in the link below)
So, theoretical anoxic stored used paper & cardboard.
3.3 billion cubic meters (harvested per year) × 20%-25% (paper/cardboard share) × 50% (carbon content) × let's say density of 900 kg per cubic meter (because the estimate is size not mass). If you returned all the paper and cardboard into anoxic storage, roughly 0.3 - 0.37 billion tons of carbon (not CO2, just carbon) could be stored per year. Mankind's production, about 8 billion tons of carbon. (I'm calculating carbon not CO2 which is about 30 billion tons per year).
So, the simple truth of it is that we use a lot more oil than we do paper. Even if every last scrap of used paper and every bit of used cardboard were all anoxicly stored, that would reduce our carbon footprint maybe 3%-4%. If you add to that, every bit of discarded wood - what then? 5%. 6, maybe 7%, and such actions would be both energy intensive and require increased tree cutting mentioned in the other answers, so there would be a fair measure of diminished returns.
A friend, who I used to debate this subject with often, had a similar idea - you want to fight greenhouse gas, he'd say, just build more things out of wood. Wood stores carbon, which it does. He was right, but we can't grow and harvest enough wood to make a real dent in our carbon footprint. Besides, when wood is harvested, and turned into furniture or a house or whatever else, energy goes into that. I'm not sure how much is even saved from the footprint by building more things from wood.
It's a good question but I think, ultimately, not practical.