Biological weathering (excreting of acids by roots) does unlock some nutrients, most notably phos.  So growing more stuff (especially brassicas or lupins) helps unlock some P from an inert tightly bound condition.  Growing more stuff also helps keep things from getting fixed again -- they are continually being taken up from the root channels of previous crops, or from the surface mulch.  Growing more stuff also prevents a huge amount of leaching, esp K and nitrate and chloride.  But we have to face up to the fact that a great many soils do not have big supplies of Zn, Cu, B, etc.  I'm just being realistic here -- cover crops can make some nutrient deficiencies worse, not better, since more is going into soil OM, and soil microbial biomass is greater.