Soil requires fertilizer regardless, every harvest you export nutrients out of the soil that need to be replenished. The main purpose of crop rotation is to avoid proliferetion of diseases and pests.
some crops replenish nutrients, e.g. legumes directly fixing nitrogen from the air.
just because capitalist industrial agriculture is addicted to fossil fuel fertilizers doesn’t mean it’s the only way to farm.
Yes they do, still it’s not sufficient enough to replenish what is needed. Agriculture is an open loop system, it requires external inputs to continue to operate. Without external inputs, agriculture turns into minery.
Cover crops can help a bit in soil that’s not seem significant agricultural use yet… by biologically mining and aerating the soil (ie. plants with deep and hardy tap roots can break through some plow pan and clay to extract mineral nutrients beneath).
Like you say, external inputs and care are needed to amend the soil to grow useful food crops. If they weren’t, we’d still be foraging, without need to settle areas and dedicate energy to agriculture.