Covering an area of grass with silage tarp or ex billboard vinyl material can work very well. You can also put all kinds of compost and inputs to prepare the soil at the same time. For some grasses it can be a long wait for them to properly rot down. Once the grass is dead and the tarp is removed a thick layer of mulch can replace the tarp.
Another method for less persistent grasses is to lay a thick layer of cardboard then put a growing medium like compost and soil over the top, put desired plants in then heavily mulch.
I agree we shouldn't be dogmatic about the use of any chemicals. Context is key and the constant tillage and constant application of herbicides, fungicides and pesticides are the real issue. I have no doubt that nature goes straight back to doing what it does after an application of glyphosate.
Bottom line is that if we want to promote better ways of farming we need to understand exactly what we are talking about and not oversell. I know of more than one person in my area who tried to plant fruit trees without removing the torpedo grass first. It is growing right up to the tree trunk & they are steadily mowing and got far poorer results than I did by removing the grass and starting fresh. I can show very good nodulation on many of the legumes I have planted even though I used about 4 applications of glyphosate, some slow release fertilizers and micronutrients. This should be my last year using the chemical fertilizer. I am setting up a large scale vermicomposting system fed by homegrown biomass, and will be continuing to make fish emulsion for other minerals not available in my soil.