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 the historical context in which many nobles left for the Crusades, often selling or mortgaging their lands, which resulted in a shift of power and land ownership toward the monarchs, thereby enabling them to consolidate and centralize their authority.