Lights plan doesn't make any sense.
He could have easily avoided L and not done anything to draw attention to himself. But the reason he fucks up and wants people to know who he is is because he wants to be God of the new world. That wouldn't work. Light can't live forever. Eventually he's going to die and the world will know. Then everyone is going to go back to being terrible and commiting crimes.
But if Light stays anonymous and doesn't let anybody know he exists then his death wouldn't matter. People would continue to be scared of Kira.