When it can be used no more, paper and cardboard rot and disintegrate. Plastic bottles don't rot for 450 years - if Shakespeare or Good Queen Bess had thrown away an empty plastic bottle it would still be around. Some plastics, like that used in plastic bags, could last even longer, up to 1000 years. If William the Conqueror had kept his arrows in a poly bag, it could still be where he tossed it away at Battle.
Paper is one of the things that can be pretty universally recycled into more paper, or into cardboard packaging, which itself can be recycled, though using cardboard boxes again and again to transport or store other goods is more sensible than using energy to recycle clean once-used boxes.
Reuse and don't overuse to start with should be the rule. When my children were young, all bits of paper that were blank on one side were saved for them to scribble or paint on. Left-over wallpaper was great for big paintings. Cardboard boxes were flattened and saved for packaging parcels in December. Now, recycling bins (and landfill bins!) are full of boxes, and sheets and sheets of almost pristine paper are thrown in, while ££££s are spent on new packaging (some of it made from those same rejected boxes, using expensive energy) and pads of virgin drawing paper, made from that same paper (using energy and bleach) .
This is the era of the throwaway society and built-in obsolescence.