Is it possible you're thinking of Super Dimension Century Orguss 02 as in this answer?
From a review of Episode 5: "Destroyer"
As they ride an elevator down, Perion tells Manning that he pretended for seven years to be mentally retarded so that Miran wouldn't assassinate him. However, on the private refuge of his small island, he discovered a massive Armor.
As you noted, the clip exists on Youtube:
The "holy men" were likely the monks, who did not power the "Armors", but did use their psychic powers to provide long-range scanning capability as per the TVTropes article entry.
Members of an order of monks are used by both the Rivilian and Zafrin militaries as the equivalents of both radar and long-range cameras, thanks to their mental abilities. However, they have a tendency of dying after overusing their powers. Nataruma has unusually strong powers as a part-Emaan, which the Zafrin military trained her to use so she could help operate their enormous Decimator.