I always reconciled that you have three possible versions of the Scourge --
"Bad" -- a Scourge controlled passively by an otherwise idle or inactive (i.e. frozen) Lich King. Granted, this is still pretty dangerous, because this is what you had at outset of the Third War.
"Worse" -- a Scourge controlled by an active and ambitious Lich King directing and controlling it toward world annihilation, but with a plan (this is Arthas from the time he wakes up in the cinematic, basically, until he is destroyed)
"Worst" -- the Scourge with no Lich King, just a frenzied uncontrolled zombie apocalypse.
Killing Arthas in favor of Bolvar was an effort to go from "worse" to merely "bad", although with some hope that Bolvar can just render them idle altogether. That's the only way I could make it make sense to myself. Fanwank is a powerful thing.