Wasn't the final result of all the Lich King quests in Icecrown that, no, he actually was just all evil? I seem to recall doing any number of quests where attempts to find any good left in him turned up negative.

Even the whole "Without Arthas the Scourge is more dangerous" resolution to the whole thing is more "Arthas is obsessed with being a king, and is thus organizing the Scourge in a way that actually makes them LESS effective rather than just setting them loose to eat everyone."