I gardened on light Cotswold Brash for nine years in the 1980s and found that no dig worked brilliantly, using mostly mushroom compost, an inch on each four foot bed every year. This was a small input for the quantity of produce, all organic. It was amazing how little water this stony soil needed and in the dry summers of 1989 and 1990, many visitors could not believe how little water I used, mainly to water plants in from cans. Although the compost dried out on top, the undisturbed soil below it hung on to its moisture and I think the capillary flow of water upwards is stronger in undug soil, because no fracturing of layers has occurred in cultivation.
At the end of every year, the compost had all gone from the surface, pulled into soil by worms and their allies, so the structure stayed good and roots found goodness at all levels.
And my seven acres were well known for an absence of weeds, one of no dig's most welcome results. There are always some weeds, but in manageable quantity.