The idea was to let them collect moisture and rejuvenate from the previous crop. With the use of fertilizer I don't believe they practice that any more. This practice may have added to the dust in the dust bowl, as a good percentage of the cropland had no covering, but laid bare. However, no-till farming is becoming somewhat popular where chemicals are used to kill growth which is left on to catch moisture, and the ground is not disturbed until planting. And yes they continue to use fertilizer.
Many farmers have acres under irrigation.
Not much wheat is under irrigation, but corn and beens are planted under the sprinklers. The wheat crop was very good this summer, and even dryland corn seems promising. The only complaint was that the price of wheat was too low. I have heard the aquifer from which most of the irrigation is done is beginning to show signs of overuse. There are numerous State and Federal studies in published form which confirm that the Ogallala Aquifer is being depleted by irrigation and pumping for human use.