My suggestion for any king of
gardening (no till or otherwise) is
not to pull plants after they are finished growing/producing. The plant spent its entire life building a
root structure as deep and massive as it was capable of. The
roots have tilled the soil.
Even in poor, hard soil, it probably managed to explore an inch or two deeper than previous crops had. This is adding life and depth to the soil...why would anybody want to remove it? There is a colony of microbes living around each root segment now, and as it dies and begins to decay, new microbes will move in and consume it, converting all of its nutrients into forms that future generations of plants will utilize.
As it rots, a foot or two below the surface, new soil life is being born around it, and also creating air pockets where oxygen and
water enter, thereby allowing worms and other critters to work deeper and deeper each year.
Every cubic inch of soil contains millions of living life forms, limited only by availability of food. If food is available below the frost line, they will migrate there as weather dictates. Billions of 'slaves' working for you...all they ask for is food.
The caveat: If you have annual crops that have been damaged/destroyed by soil-borne disease, I strongly suggest that you remove as much of the plant as possible (and do not replant that species nearby for several years)
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