That might be true, but to establish that state we'd have to kill off the native grazers. People tend to forget that before we had vast herds of domestic cattle in the western plains we had vast herds of bison, antelope, etc.
I read in some book on pre-Columbian history or other that the prairie that existed in North America when Europeans first showed up was a product of human activity. It seems that folks living in the Great Plains started burning down forests to create more grazing land for bison, in order to have larger bison herds for hunting.
re: antelope, I thought they were browsers and not grazers.
https://www.earthfix.info/news/article/juniper-trees-sage-gr...
And juniper trees aren't exactly a 'forest' like most people would think of one.