system
Given the following post, respond as if you're commenting on Reddit:
human
[Death Note] If Light does nothing during L's broadcast...

If Light had decided to do nothing or maybe wait awhile reacting to L's broadcast with criminal stand in, how much would have changed? I'm thinking maybe he decided to wait a few days to a few weeks before writing down the name. That should have given Light enough time to find out that the broadcast was only being shown a certain times at certain places.
gpt
The broadcast allowed L to pinpoint Kyra's location to the Kanto region of Japan. "Pinpoint" is optimistic, though, because with a population of 45 million, you aren't going to find Kyra just from knowing he's in Kanto. Even the additional piece of information that Kyra must be a high school student is near useless. What's L going to do, check millions of students in Kanto?

The key which allowed L to have a chance of catching Light wasn't the broadcast trick, it was the fact Light changed his killing schedule after hacking his father's computer to find out L knew about him being a student. From that, L deduced Kyra had to be connected to a high ranking police officer, DRAMATICALLY reducing the list of suspects by millions. The important part is that Light *knew* L would realize he changed the schedule on purpose; he wanted L to get close to him so he could find out who L was and kill him.

So the issue here isn't that Light was afraid of L catching him. Having access to his father's intel meant Light would always be a step ahead. If he *wanted to*, L wouldn't have caught him, ever. For instance, if he had waited say two weeks then changed his schedule slightly (say, all killings on Thursdays that were happening at 8 PM now happen at 6 PM), L would just think the student had a slight change of routine; since it wouldn't match Light's routine, he would never be caught, even if L looked into every single Kanto student. So in the beginning of the story, Light getting caught was never an issue. He was under no danger. But he wanted to *defeat* L, not simply *evade* him, which required taking controlled risks to have L approach him.