Hi Parker! Thanks for your comment!
There are actually different trade-offs in the sustainability and environmental impact of free-range and feedlot beef. In this report by Oklahoma State University, they discuss how feedlot cattle have a lower carbon footprint than free-range cattle. However, they also discuss how free-range cattle contribute to a more sustainable beef economy because they consume plants that are inedible to humans. You can read the report here: https://extension.okstate.edu/fact-sheets/carbon-footprint-comparison-between-grass-and-grain-finished-beef.html
While there are definitely pros and cons to each form of cattle raising and their associated environmental impacts, there is without a doubt an answer to completely eradicating the carbon footprint of the cattle industry and that's switching to a plant-based diet.