Bacteria probably need the right conditions to efficiently break down materials, cellulose is quite tough.
Some landfills capture the released methane and burn it (to avoid atmospheric pollution), which seems like a decent solution (even more with power generation). Some of the material will remain undecomposed (or take a really long time) so it is a net carbon sink. I think this depends on properly sealing landfills and arranging extraction infrastructure.
Seems like a good resource:
https://www.epa.gov/lmop/basic-information-about-landfill-ga...
Another idea would be to curb methane generation or decomposition somehow. Apparently aerobic decomposition reduces or prevents the release of methane:
https://www.agric.wa.gov.au/climate-change/composting-avoid-...
Burning trash directly is also an alternative I guess, though one I'm not very comfortable with due to trace elements contained in everyday items -- surely some mercury and heavy metals will sneak into residues? (and then into the atmosphere and our lungs)
Now, of course, we have LEDs in place of CFLs, and coal burning power generation is on the way out, so it's all moot.