I pasture my own stalks in my crazy grazing standing corn system. Some strips have been winter grazed corn on corn for 6 or 7 years straight. And the improvement in my high clay rocky SW WI hillside fields and soils is amazing. They lose amost zero soil to rains.

I think one key is to do most of your grazing after the ground is frozen to avoid compaction issues. I have had very little issues with compaction except in lanes and in front of gates, etc. But on the advice of a very good C IL customer am trying an Aerway on the grazed corn on corn.  It is still a work in progress but looks good.

A very good large scale E IA customer who has taught me a lot has many acres in strip tilled continuous corn for over 10 years and his soils keep getting better.

And the better/healthier/higher OM your soils get, the faster residue seems to disappear - as in the OP.  But that is a good thing. worms like their supper on the surface, not mixed into the soil profile. In return they distribute their manure vertically and aerate and provide drainage and root paths even in heavy clays....

Heavy pasturing of stalks will help - but you need to not cause undue hoof compaction. Or take some steps to aleviate it - esp if you are not in a deep frost area (WA?). The Aerway may be the tool to run. After getting the cattle off of the stalk field in the spring, spread whatever dry fert you need (if not applied in the strip) run the Aerway at a steep angle to the stalks then strip till with at least N & S between the old stalk rows. The old stalks are still attached to the ground to hold soil.  jmho.

Jim at Dawn