The whole point of no dig is you don’t want to break up the soil - the soil has a complex structure and a whole interlinked network of fungi, bacteria, teensy animals that are all super important to transporting nutrition and water to plant roots. That's very true, but I see very little difference between disturbing the top layer of soil to get rid of the turf; and leaving it intact and covering with a very disturbed layer of compost. In either case, the fungi/bacteria/invertebrates will need to get established.
It's really interesting how ideas have changed in my lifetime. When I started gardening, the ethos was to double dig every year, sterilise any soil that was being used in pots, and use chemicals as a prophylactic - spray to prevent, rather than to get rid. Organic gardening was regarded as a fad entirely without scientific basis.
Then it was discovered that terrestrial orchids were really strange - they had a symbiosis with fungi, so couldn't be grown unless the fungi were already there.
Now symbiotic fungi have been found to be important in over 90% of plant families. RHS and Gardener's Question Time are no longer recommending you spray your garden into oblivion, soil sterilisation is no longer a routine, and most of the chemicals available to gardeners in the 50s and 60s are now banned.
There are still problems. Why are we still using peat for recreational gardening? Why do so many people routinely use so many weedkillers on lawns, over fertilise them, and even use worm-killers? Why, when the effects of too much nitrogen in our rivers and on our wildflowers are clear, are we still recommended to apply fertilisers regularly to plants that are growing in the ground?