The statement that best analyzes the impact of the Crusades on the role of European monarchs is: "Monarchs were able to expand their influence as nobles fighting in the Crusades sold their lands, which allowed the monarchs to centralize their power."
This statement accurately reflects how the Crusades affected the power dynamics between monarchs and nobles, illustrating that as nobles left to fight or sold their lands, monarchs could consolidate power and resources, thereby strengthening their own authority and centralizing governance.