author=VirtualVampire
If Light had done this the world would have become a better place, because the people with power would finally have someone to answer to for their crimes.
Although I must say I don't agree with eliminating the rotten from the world, indeed if Light had done what you said he should've done, rather than what he did, people would've loved, not feared him, and the world could've started moving in the right direction, assuming he would walk the Earth as no more than a human being.
The main problem is, this was never Light's intention. Because of his extreme intelligence, and him excelling over anything and anyone, he quickly came to see himself as superior to them. Combine that with him being bored to death because nothing was challenging to him. He excelled with the ladies, and even at sports (tennis) so his life was really monotonous. When he found that Death Note, he didn't think about the world, and how he could change it. That was just a lie he made himself believe in. The only thing he was ever after was being God. Even if he had killed all corrupt leaders in the world, and spared the purpetrators of lesser crimes, it wouldn't have changed a thing. He would still have ruled the world as God and people still would've lived in fear of going against his wishes. The law can never be in the hands of one person. Even if Light had been righteous at first (which he wasn't) he would've gone mad with power in a matter of months. From there, it's a small step to killing dozens of police agents, anyone opposing your will, and eventually his own father.