I sort of understand this, and I sort of don't. There's a sudden change there, for sure, and from what I hear not a lot of people stick through the shift in the story's focus.
When I first watched the show I had the same kind of reaction to Light and L and the early story. But after a while, I started to understand what the writer was going for. So when that same sort of thing started happening again later on, I went with it.
Spoiler: Death Note symbolism and stuff
Show
I actually really like the second half. It's depicting that although Light had won the battle, he was still nailed down by the compromises he had to make in order to get that victory. He was going to have to continue being careful in a post-L world. Both against people seeking to take up L's mantle and those seeking to take Light's position.
It's really all about how Light's ideal world is ultimately arbitrary and doomed to failure. Although Light beat L, Light will inevitably lose and whoever comes after won't continue what he's done.