Jake,

Soil structure and aggregation are strongly associated with productivity (crop yield), ability to resist erosion, ability to infiltrate water, etc.  Soils with no structure are called roads.

As for the comment about occasional favorable yield responses to certain flavors of tillage, you completely missed the point of my post.  Most of agriculture is currently a mining process, especially if tillage is used.  Harvesting grain removes much more than N, P, K, and soils have limited reservoirs of the other nutrients.  If you are verging on a problem to the point that a little tillage hides it, you will soon be in the realm of serious deficiencies.  Best to address the underlying problem before it gets any worse.