Well i have been thinking about this for a while now and I have come to a conclusion that we are not fighting arthas or nerzhul in this entire xpac but Frostmourne itself. I did have this thought a few months ago back in 3.0 after really thinking about it but stepping into the Frozen Halls and ICC itself has really shown me that this is the case.
In the Arthas book the Lich King had a mental confrontation with Ner'zhul and Arthas, and i was like WOAH...woah woah who is that then talking to them? So next thing we all know Ner'zhul gets slain and arthas got "slain". So then if thats the case then that means neither of them exist even in this so called fused form that was supposed to be created when Arthas put the Helm of Domination on his head which is allowing Arthas to actually control the scourge. If people look at this artifact itself one will see that this helmet was what held Ner'zhul and granted him his power, so in this case Arthas as a last ditch effort is storing his spirit in the helmet to hold control while Frostmourne acts on its own.
I say the new Atiesh because the quest chain for Atiesh had you purge it of an evil demon that was housed in it when Sargeras possessed Medivh. This demon remnant in Atiesh and what ever lurks in Frostmourne are very similar. Why do i say something lurks in Frostmourne? Look above...
Now lets think here, if it were up to Frostmourne the zombies would run rampant destroying all, sounds like a legion tactic to me. Arthas is using all the will power he has through the Helmet of Domination to control each and every scourge, hell it would not surprise me this entire time he was fighting off this sword. The Nathrezim and Frostmourne could not even combined break his spirit, if that's not the sign of a true strength i dont know what is. But in all honesty Atiesh and Frostmourne are pretty much the same thing in essence, both parasites.
My huge question is what resides in Frostmourne? An assumption is apart of Sargeras, after he was split in two you could say during the war of the ancients his essence was scattered and quite honestly he was weakened to such a point that even Medivh's mother could beat him in combat. He then goes and possessed Medivh and after that god knows where he went, again it points to Frostmourne. It just seems to be his style but the reason again why he cannot even gain full control is because Arthas though his soul was trapped by the blade also fused into the Helmet and now could technically reside in the helm itself thus at a ground zero to focus all energy to fighting Sargeras or Frostmourne.
In conclusion, arthas is good, frostmourne is evil and what ever frostmourne is it shares every trait of a parasite or at least a demonic parasite. GG for being possessed.