Other arguments for tilling exist: aeration, mixing-in of new organic content/fertilizer (not really necessary: green waste can just be dumped at surface level in many cases, and this is already becoming more common in mass-agriculture with 'cover crops'), furrow-creation for seed planting, etc.

Fundamentally, leaving a field uncovered for any length of time is bad and destroys the soil more than if you'd just let it grow weeds or a temporary crop for awhile then culled that as in-place fertilizer for a next crop.

A few months ago some friends of mine visited Australia from overseas and I took them to one of the older wineries in the area. The winery manages something like 10-20 major fields. They brought in a new viticulturalist to manage the fields and the first thing he did was introduce cover crops. In the tasting, they brought out soil cores from before and after the changes, which had only been in place for two years. The difference was tremendous. The old methods, unquestioned for decades, left the soil dry, poor, and largely infertile. The new methods restored organic matter, moisture retention, and a significant sub-surface biome.