I don't think you'd miss anything substantial. He does a good job of telling the history and (I think) avoiding the assumption that the reader has with them a deep cultural knowledge of how americans eat now and in the past.
Rather, for each of the four meals he follows he asks "How does the food chain underlying this meal work? Why is it here?". When I say it's American centered, I mean that the answers to these questions are very intertwined with government policy and location.
So for the first meal he talks about Corn a lot because america grows a shit ton of it, but the story he's trying to tell is that of industrial mono cultures. The story about mono culture is interesting in it's own right. But the path he takes to it is local to me. I live in the middle of the systems and ecology and people he is describing. When he talks about field runoff from the chemicals needed to make a corn mono culture work, he's talking about something that directly impacts me. I've swam in those waterways. I've fished in them. They're where my tap water is drawn from.