The separation was the fault of Emperor Diocletian, who controlled the east while choosing Maximian to lead the west. That was a wise approach because the Western Roman Empire was doomed in the end. It was destroyed by groups such as the Visigoths until its last emperor was toppled in 476 A.D.
This makes the Byzantine Empire’s achievements all the more amazing, as it would survive its counterpart’s fall and persist into the modern era. In fact, no other country west of China could pull it off. The empire’s wealth and relative political cohesiveness allowed it not only to endure but also to grow.