Weeds are a conundrum for most people. But as I walk around in my yard, I find plants that are edible, beautiful and useful. But I totally get how you feel. I work on removing the non-native stuff, for now. And I have a particularly nasty one: Lesser Celandine. Then, there's dead nettle, from Europe and Asia, and jewelweed, which is native to the northeast, but it goes crazy. I keep a hedge of it for the hummingbirds and pollinators, but remove the rest.
Image: Ohio State University.
But this is off the topic. If you have only native "weeds", (as I understand that book), your garden should be able to thrive among them if you prepare the field as the author explained, with minimal work, no tilling, just mulching with straw and cover crops. It's the idea of co-habitation, I guess. The book has a spiritual element, (not religion), more like oneness with everything, and working together.
I have lesser celandine here, but it's not been too much of a problem. I like its bright yellow color in the spring. I also have dead nettle, and the trailing variety has caused more problems than the upright one. And jewelweed, well jewelweed is supposed to grow in the vicinity of poison ivy, as it is an antidote. We have poison ivy and we have jewelweed, but it's not much of a problem either.
The plants that were problems were dock and a few I don't know the names of, but have been contending with for years. I don't mind the weeds in the yard, in fact, there are more weeds than grass in my yard. But I don't want them taking over the veg garden like they did last year, with the connivance of the clover cover crop!