As we are no-diggers we can just debate the no-dig part of your post. All vegetation has growth within the soil as well as top growth and I remove only the top growth to the compost bin. The roots do much to improve soil structure and fertility and some green manures harvest minerals from deep down in the soil.
Pet Budd and others have argued the case for using green manures to create sufficient compost to apply to beds as an alternative to importing organic content via deliveries of municipal compost or farmyard manure. Pete is able to be self sufficient in compost by using 1/4 of his plot for green manure while others advocate using 1/3 of the plot.
This question has actually been debated before. See this article
I wrote in an earlier post “I have been inspired by a writer who had several plots close to mine between 1970and 1990 and he used his plots to try to answer the question ‘Can a given level of food production be maintained, or even increased, with systems that are, as far as possible, self-contained?’ He grew green manure rather than using imported compost. Charles has his book, ‘Questioning Garden’ by Nic Pawson and his ideas have also been published in Patrick Whitfield’s book, ‘How to make a Forest Garden’ seen in the margin on this page.