Emperor and Divine Beasts needed to eat as well since the Unwavering Loyalty array granted them nigh-immortality but was helpless against hunger.
Both sides knew that the first to strike the food reserves of the others would also be the winner of the war.
Vesta, instead, was the main hub of the Dimensional Gate system, holding the database of the coordinates and passwords for every city Gate. Without it, transportation between the cities would be much slower because mages would have to input everything by hand each time.
Also, without Vesta, Royal Override codes would become meaningless and Thrud would gain full access to the Gate network. Even without the passwords, she would be capable of finding the secret bases of the army and the Association just by consulting the database of the dimensional coordinates.
