He was trying to prevent future crimes by making people afraid to commit crimes so it wasn't as simple as just getting rid of specific people. Light was a brainlette in the end though. The Death Note's most powerful ability wasn't killing people it was controlling their actions before death but there is no rule that says you couldn't repeatedly control someone's actions and set the death to exceed the time limit. This would allow for controlling government leaders and capitalists until they die of old age or exceed usefulness thus obtaining the ultimate power for change. Instead he used it to stroke his sense of his ego filled sense of morality and kill whoever he saw as undesirable.