Here is another possibility. Karthus is a creature spreading the gift of undeath throughout the world. If he had a spell that insta-killed everyone, everywhere, at once, he could sing the whole song and obliterate everyone at once. Thus beginning the work of creating 6 billion undead.
6 billion/everyone in the entire world may sound like a great deal of undeath, but remember, Karthus is effectively immortal. Everyone in the world may not be enough. Undeath can only come after death, and death can only come after life. So his fighting within the league (an organization designed to stop wars) may be his way of preserving enough life so he can make even more undead.
To an immortal, they may plan centuries or even millenia in advanced. Karthus might have the power, simply not elect to use it.