The ending is the biggest plot whole in the whole show. Did he actually die? The answer is so vague its still freaking debateable!
Meanwhile, the ending doesn't actually make sense.... he dies, so all corruption ends??? As long as there are greedy people, there will always be people who abuse power..... a highly hated person dying isn't going to change that. In reality, his death would've realistically plunged the world into total chaos. With no nobility, the Brittanian Empire would've had massive bloodshed before a new Emperor rose to power. Meanwhile, the Alliance would've collapsed as members tried to fight for their own advancement.
His death really, instead of causing peace, would've only caused far worse bloodshed than the massive bloodbath of a final battle he led.
The vagueness of the ending is intentional; the viewer chooses what they want.
If you don't think the ending makes sense, then you haven't paid attention. Within the first two minutes of episode one, we are told by Lelouch himself what he wanted to do; destroy Britannia. And he did. He painted himself and the image of Britannia to be the Devil, so when he was killed, he took that Britannia with him, and left Suzaku to pick up the pieces.
And you are forgetting two more very important factors that would stop bloodshed from happening:
1. Britannia was the world's common enemy. I say the world's, because nobody in Britannia liked Britannia under Lelouch's rule.
2. The only person with enough power to take the world for himself is forced to work under Zero.
Lelouch is smart enough to know that corruption will not fade, in fact he chooses a world of corruption when he kills his father. The show never says that he ended corruption, either, so your argument really doesn't have much ground. He made a better world for his sister, and he destroyed Britannia. His mission: accomplished.
He destroyed the world and created anew. He destroyed Britannia, and left a new one in its place. No single nation just went *poof*. Nunnally is the 100th Empress, remember.
What you said about his sister is absolutely true, which is quite the tragic irony, and it was well placed, too. When Nunnally told Lelouch about that, it was too late for him to stop what he was doing. This doesn't take away from the story, but adds more depth and tragedy to it.
Suzaku is there as Zero as a symbol of justice, and since everyone got behind him due to his killing the Demon Lelouch, a symbol of unity, as well. He doesn't have to guide the world, but only don the mask, and the world will carry on itself. And when his time comes, another will replace him as Zero. For Zero is not an individual, but a symbol.