10 years ago or so I saw plastic wapped bundles of shredded cottonwear in the shelves at a mechanic shop I frequented at the time so some of it clearly has taken that path.
Rags were and still are a useful item in industrial shops as they are stronger than paper towels, don't fall apart, and handle sharp metal edges and rough surfaces.
In the old days a "ragman" would come by your shop and buy/sell scrap fabric for rag use. When I was a kid in the 80's I distinctly remember a man pulling up in an old truck and my father buying a few boxes of rags for his machine shop, rummaging through a few boxes looking for the ones with the larger sheets and heavier material.
At home I have a bag in my basement full of old clothing I use for whatever. I even wash them if they're not covered in something which could foul the washing machine (e.g. automotive grease/oil/fuel).
Until the late 19th century, paper was more frequently made from rags than wood pulp. The switch to wood pulp was because paper demand outstripped rag supply. Perhaps it's time for a return to increased rag content in paper.
Yeah; from time to time we reuse old t-shirts or bed sheets and turn them into handkerchiefs. We do use a lot of handkerchiefs with a small child :). But also other things, eg my wife took a pair of old jeans and cut off all but the waist+pockets -> an extra pair of pockets while lab'ing at work.
This is common knowledge in developing countries (and, I suspect, used to be in developed ones a few decades ago). Growing up, the usual lifecycle of a garment was wear -> rag -> trash.
