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 highlights how the reduction of noble power and the acquisition of land by monarchs contributed to the centralization of authority, which was a significant development in the political landscape of medieval Europe following the Crusades.