You gotta wonder just how petty he got about it, too. He did mention bumping off "worthless and lazy" people, too, but not as obviously. So how long do you think it took him to go from murderers and rapists and robbers to petty fraudsters and drug users? You think Light would kill someone who had extenuating circumstances in their case? What if it's just some shitty douchebag kid who pulled a prank and got a criminal charge for it? Light was thinking of killing people in his class just for being dicks, so would he kill someone like a nuisance streamer or some random jackass? How long do you think that'd take?
In part 2 Takada pisses off Light by announcing too early that they werw going to start targeting shitty people who weren't necessarily serious criminals, but that implies he'd eventually do that openly.