I'll play theory machine, though IC I admit my characters are not working towards the betterment of mankind.
My main contention is that this is actually a control movement for Overlord, and that he has political reasons which do not involve humans for needing a war with the humans as an expansionary war.
I'll also suppose that the war with the Undead was not "won" so much as stalemated, as a true victory is likely impossible. In effect, removing the human realms has as much to do with denying the undead future soldiers as wanting slaves for his own purposes.