Anime

No kidding, like he really had to fuck up hard to get caught doing what he was doing. The guy anonymously makes himself the executioner's blade of the global capitalist police state. The mainstream news and imperial core policing institutions publishes lists of names labeled "criminal". Light Yagami kills them. Kira's will and the will of capitalist states the world over were aligned.

Light kills various detectives during the initial investigations, but there were absolutely 0 serious police or societal resources put toward stopping the threat of Kira until L chases Light into a corner. To lose the heat, Light has Rem give the death note to some dumbass rich executive who starts using it to kill other rich people, and the hammer comes down. Then once Light gets the death note back, Rem, a literal goddess of death, sacrifices herself to kill L and bailout Misa. Light comes out of this squeaky clean.

The first incident with L, chalk it up to inexperience with the real world. Light starts his career as a magical serial killer a young man fresh out of high school, stupid mistakes are expected.

After that? There's never another serious attempt to stop him until he gets too cocky and slips up several times while being watched by a rogue CIA offshoot lead by a literal 12 year old. This rogue CIA offshoot had by that point lost all state backing. The president of the United States himself by that point expresses support of Kira. Light Yagami was just sort of a fuck up.