Wasn't he making sure to show a pattern as a warning for criminals so they would stop? He intended the legend of Kira to exist.
It's been a while but if I remember correctly, L set up a trap for him and Light fell for it (killing a guy passing as L on Japanese TV). If Light didn't fell for that, L would have repeated the live transmissions in other places in the world. He was expecting the culprit to do a display of power.