I would personally write it this way: "Some people are apt to claim that historical buildings are living history. However, even if we take into account the architectural value of an ancient cathedral, it would save the government money to rent out these monuments." "Apt to" is more natural than "prone to." "Living history" is more natural than "live history." "The architectural value" seems more natural, because it parallels the idea of monetary value. "To rent out" seems more natural to me than "to rent."