Newspapers are worth recycling, because they can be turned into new newspapers again, removing the ink and the metal can be done fairly efficiently.
Cardboard can be recycled fairly efficiently, and can be turned into new cardboard.
Plastic-covered/glued/glossy/window envelopes/food containers/other contaminated papers can't be recycled. Just incinerate it, or turn it into pellet fuel and incinerate it.
What chemicals are involved in that process?
Is cardboard similar?
Does this take into account the logistics costs?
Recycling newspaper is a no-brainer from a cost perspective. You can't recycle forever though, each time you lose some wood fibers that are too short and have to be removed from the recycled pulp, so you have to add fresh pulp.
Burying old newspapers in the ground is a form of carbon sequestration. Really it comes down to what takes less energy: cutting down the trees, or the transport, sorting and reprocessing of old newspapers.
So like I said, it's a no-brainer to recycle newspapers.