Why do we recycle paper?
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?


You are ignoring a number of factors here.

A good deal of energy, much of it non-renewable, is needed to turn trees into paper. The trees need to be cut down (requires petroleum), transported to the saw mill (more petroleum), sawed and chipped (requires electricity), transported again (more petroleum). Once it gets to the paper mill, it needs to be pulped (requires petrochemicals, which need to be transported (requires petroleum)). The pulping process also consumes a good deal of electricity, as does the process of turning pulp into paper.

Bottom line: Paper has a positive carbon footprint.

If you send that paper to a landfill after using it, the carbon in that paper will be released to the environment, and in fairly short order. On the other hand, recycling paper bypasses a number of the steps involved in turning trees into paper. Turning paper into pulp is easy. Recycling paper reduces paper's positive carbon footprint by a significant amount.



The question specifically asks about finding a method of isolating wastes from the effects of weathering. That's not easy. Anaerobic bacteria find paper to be quite yummy. A deep ocean trench might work, but it would be better to not make paper in the first place. Growing and harvesting trash trees and then sending them into the deep would be more effective. A number of early geoengineering proposals suggested doing just that. There are big problems here, mostly unintended consequences. Deep sixing trees in deep ocean trenches is no longer viewed as a viable carbon sequestration scheme.