Not really - I mean, you've seen firsthand how powerful the PC/Champion is and otherwise can be, why wouldn't the Lich King want a veritable army of super-powered soldiers working for him in the Scourge. Arthas wasn't "fighting against the Lich King's will" because as of "Rise of Lich King" he'd completely extirpated Ner'zhul from his consciousness and essentially destroyed him - Arthas was the Lich King at that point, not a separate entity fighting for control. This isn't to say there couldn't be a better version of the story, either; I'm just saying that between the two options of "Arthas lures a bunch of heroes to him to try to corrupt them in a perverse version of what had happened to him" and "Arthas leads the Scourge on another ho-hum invasion that the Horde and Alliance repulse" the former strikes me as the better of the two stories.
Not to say it doesn't have issues, but it's still both thematically and dramatically better for the game itself in my opinion.