Seems like a lot of people are misunderstanding some things...
It's not that he wanted to die, but had no choice to die.
The order to "protect humanity", was starting to twist him. It made him want to destroy humanity to save it. He knew that he was the evil that needed to be destroyed. Hence, the reason he needed to die. But now that he's able to suppress that order, it no longer matters.
He said it more than once... "I don't want to die."
While I agree that being "immortal" will make him suffer again, but maybe they might find a way to let him grow old. The philosopher stone is the source of his power, right? Then they just need to figure out how to take it out and turn him into a human. While it sounds easy, it probably won't be. But I think this is what the mangaka is aiming for at the end.