Except he kinda did.
Whether or not he made the right design when it came to purging Stratholme, he was pretty much screwed, either way, and Mal'Ganis gets what he wants.Arthas: Listen, Uther, there's something about the plague you should know.
{Sees that the people of Stratholme ate the tainted grains}
Arthas: Oh, no... we're too late. These people have all been infected! They may look fine now, but it's just a matter of time before they turn into the undead!
{...}
Arthas: This entire city must be purged.
As for whether or not Arthas should be judged for his crimes when he took up Frostmourne (if he had total control, or was subtly influenced or fully brainwashed by the Jailer), it is tough to say. We'll have to see how it'll play out. Blizzard is free to retcon their story however they please (it doesn't mean they should, though).
I wonder if the characters in-game will even bring up the discussion of culpability on Arthas' part if they discuss Anduin not being in his own mind when he attacked the Archon.