Thank you for your thorough post.
There are alternative models, such as biocyclic veganic agriculture, or in the future, foods created through fermentation [1] (this almost require no arable land). I recommend checking them out if you are interested in cycles in nature. Using animal manure, opposed to "plant manure" from nitrogen fixing plants, it also has its downsides because of the high levels of ammonia it kills most of the soil creatures such as worms, and more tilling and maintenance is required (which releases more carbon).
Personally I don't think that using livestock is living with nature, but is its antithesis. Since the earth is (at this moment) bound by the amount of biomass available through photosynthesis there is a limited carrying capacity for biomass. What we have done specifically is reduced the biodiversity by using more and more land mass for livestock and its feed. Of all habitable land, 50% is used for agriculture and 77% of that is used for livestock (while only providing us 18% of calories and 37% of protein) [2]. This has drastically reduced the number of wild animals and biodiversity, which I consider "nature" [3].
Ultimately, using livestock kills living beings (primarily in nature) somewhere else. If you're goals are living closer to nature, and reducing your ecological footprint, and your definition of nature is: "the phenomena of the physical world collectively, including plants, animals, the landscape, and other features and products of the earth, as opposed to humans or human creations.", then living closer to nature would mean rewilding your land and perhaps be a steward of that land. It would be a great means of treating nature and life with more respect :).
[1] https://www.theguardian.com/environment/2021/jun/21/microbes... [2]: https://ourworldindata.org/uploads/2019/11/Global-land-use-g... [3]: https://peakoilbarrel.com/wp-content/uploads/2017/11/Terrest...