I'm sort of in-between dig and no-dig.
My raised beds are initially filled with bulk municipal compost on top of cardboard., laying on mineral soil (sandy loam). After the cardboard decomposes, worms move mineral matter upward from soil into the beds, but also move organic matter down from the compost.
As the compost in the bed ages, I find that it needs a good turning with a spading fork. That is usually because the upper part of the compost in the bed has lost its water-holding capacity as fine material works downward (worms and insects do that). Turning usually brings some mineral matter (sand, silt, clay) up from the underying soil, and that is highly beneficial, IMO. I do this when I notice the bed seems to need watering more than it should, about every other year.
In some of my raised beds, turning the bed, and a little underlying soil, is easy. Other beds require swinging a pickaxe to move some of the mineral soil upward, due to the hardness of the soil. Worm action improves when the worms have a little help.