Soil depletion...? How in the world you deplete soil by adding nutrients through fertiliser?
"Chemical-based farming" is a lot more than just adding fertilizer.
Clear-cutting and deforestation to make farmland. Increased crop yields extracts more from the ground. Increased extraction of groundwater. Erosion due to killing of weeds, heavy tilling, and destruction of forests and native plants. Phosphate mining makes a giant mess.
No, in comparison to many other mining activities, it's a much smaller size of a mess.
Soil depletion via intensive agriculture is a pretty well established thing.
If there is no nitrates, and phosphates in the soil, they can't magically appear out of nowhere.
Organic farming aims to fall in the middle somewhere.
There is a law of preservation of energy. Elements don't transmute into each other, and don't appear out of nowhere.
The mass of biologically available nitrogen, and phosphorus in the harvest is equal to the mass of nitrogen, and phosphorus removed from soil.
No way around this. When there will be no nitrogen, and no phosphorus, there will be no crops. There will be no material for plants to use to make its cells from!
The "Organic agriculture" crowd sound to me very much like antivaxers, except fighting the agriculture industry.
This is simplistic to a fault. Legumes, for example, fix nitrogen; we've known for thousands of years about crop rotation.
Runoff and erosion - processes that tend to be sped up by industrial farming techniques - cause phosphorous depletion in a way not due to the harvest itself, as well.
There are a lot of factors in soil depletion. Some are under our control, via different farming techniques, changes in density, etc.
But in a nutshell - plants are in a symbiosis with the microorganisms and fungi that live in the ground. Plants feed them sugars and they feed the plants nutrients in return.
When you add large amounts of artificial fertilizers, plants don't need to feed these organisms anymore and this soil fauna dies. But the soil fauna also normally excretes materials that improve soil quality (e.g. fungi excrete glomalin, which binds the soil particles together). So if you use artificial fertilizers for a long time, your soil becomes dead. And such soil is easily depleted by wind and rain erosion.