> But how do you kill the cover crop so you can grow wheat again? How do you kill the weeds? ... The only viable answer today is...Roundup (glyphosate).

I don't agree, and I note that you also answered your question differently later in your post with the note about 'mixed farming' (grazing it off).

There are, of course, other answers than herbicides. Seasonal crops, harvesting and then seed-sowing amongst the stubble (provides some mulch & eroson protection), intensive strip-grazing (bovine, ovine, caprine, or fowl, all effective options), or even a cycle or two of fallow.