Good Q. Since there are many wetland plant species and willows that are beaverlike you could ask how would they become established in the first place, and how would their growing mass and persistence compare to a beaver's after a catastrophic event? And after all, why does the dry deep-gorge Southwest look like the Southwest anyway? THAT could be the outlier and its depth and dryness would seem the result of a 'jump start in erosion' bestowed over geologic time. I think even the Southwest may have been on course to be as green as the East and would have been -- had it not been for some truly horrific floods that eclipse anything in the modern era when the plugs for Glacial Lake Missoula and Bonneville gave way.

Drainage paths in the West ( https://i.dailymail.co.uk/i/pix/2016/10/21/16/3995911F000005... ) were more narrow and violent, the same in the East were not. A minimum of sudden deep erosion and therefore sideways diversion of blocked watercourses would be necessary for beavers to get established and shape the landscape so in the East they did. Other places in the world like the Amazon may have been shaped by vegetation impeding erosion more so than gnawing creatures.