He also decided to kill thousands of low-level criminals instead of like ten rich people.
Imagine one day a mega-billionaire has a fatal heart attack. Found in his possession is the name of another mega-billionaire, scrawled onto whatever was near them in their own blood.
The next day, that billionaire drops dead. Another heart attack, another name found near the body. Rinse and repeat.
Eventually, one gets smart. Publicly pledges to give away their entire fortune and take an oath of poverty the day their name is found. The reaper skips him, and the message is sent: if you're ultra wealthy and want to live, stop being ultra wealthy.
Sure, it may not be foolproof: there's probably a lot of super rich people whose identities are more or less private. Maybe one of them can pull a fast one & hide their wealth rather than give it away. But still, it'd probably be more effective than what Light did with less killing to boot.