If he did that, he'd be hurting the people the wrong way. He didn't want to fight against them. He needed a target for the hatred (himself), and someone (Kururugi) to lead the people towards that (the Britanian Government). They still have to fight against that, and Kururugi's leading them that way. But like I said, Lelouch didn't want to fight against the people, just take in thier hate.
It all makes perfect sense to me.

That's why Kururugi is Zero. He's there to do what Lelouch was doing, to take his place. He can't go back to being Zero, so someone else had to take his place. Plus, if he stayed alive, all that hate would eventually reach a boiling point, and terrorism would start against him.
But honestly, the anime leaves us with a 'happy ending', and that's all we know. Unless they make a third season, there's no way to know for sure if everyone would turn on each other again or not.

Except that at the end of the anime, he said that the blame for all the bad and hate, was directed at him as the emperor. He still gets all the hate and blame, even in death. Also, Kururugi became the new Zero to combat the injustices, and guide the hate. (Really, no matter what, there's always going to be 'petty little hates' regardless of what's happening, or who's in charge. There's no way to obliterate that.)

Sooo, Zero. Last episode of R2.

If anything, he made more sense. I admit, he was a cooler being a psycho (), but I find nothing wrong with it. Sure, dying isn't something you expect him to do... and yet that's everything he ever did. He was always doing unexpected things, and this was really no different.