Light Yagami's desire to rid the world of crime and corruption is primarily fueled by his strong sense of justice and his belief that he is the only one capable of bringing about a perfect world free from evil. His intelligence and idealistic views lead him to believe that by eliminating criminals through the use of the Death Note, he can create a utopia where only those he deems worthy of living are left. However, as the series progresses, his motivations become more complex and darker, revealing a descent into megalomania and a desire for power and control.