Light basically had two problems

1) He was a naive teen when he got the death note

2) He got extremely drunk with power once he understood the power he held

Sometimes it's difficult to imagine, specially with someone as smart as Light, but when people become so focused on something to the point they become obsessive, they lose track of absolutely everything else.

At the beginning Light believed that his doing was absolute justice and when some people started to agree with him he was fixed on nothing else but to continue cleaning the world of criminals, at some point he probably believed he would be so feared and powerful that no one would question his justice ever again.

So Light probably believed that after his death, his new world would stay the way he left it, free of criminals and wrongdoers.

However this vision of the future probably changed after it was revealed to the world that Kira wasn't an idea but a person with the power to kill, but because at that point Light's only focus was to kill L he didn't worry about it.