They have to, he's a serial murderer with a god complex. Cops are paid to stop those guys.
But anyway, if Light were serious about his principles he'd kill select people in subtle fashion, influencing society by increments to make a better world and keeping himself out of the limelight so he could continue his work uninterrupted. But he's not serious about his principles; he's just using them as an excuse to boost his own ego and, well, we see where that gets him.
I do wonder what Near and co. would do with the Death Notes, though. Or would Rukh just reclaim them once Light's dead?