Eowyn being the best hero killer in the game is quite frankly - bullshit. Killing the Witch King? Okay. Questionable. Killing Gorthaur? What? Killing Sauron? Alright, whatever. Why is she the best? It doesn't make any sense whatsoever.
As this is a balance related topic I'd like to share some thoughts.
You say Eowyn is a good herokiller.
Well, we can agree on that, it's her job after all. Every hero in the game has a certain function, like Gandalf beeing a mass-slayer or Dain a unit supporter. And Eowyn is a herokiller. So I think there is nothing wrong with that.
Then you say she is THE BEST herokiller in the game (which she is not, but she is very good), and I think that means you think she is TOO GOOD.
And here I don't agree.
As I said I think Eowyn is a very good herokiller with very powerfull abilities later on (lvl 5 and lvl 10). But the important point is, she is only good vs heroes. Eowyn has no ability that really helps her against normal units. Other herokillers, like Aragon, are very effective against units as well. Eowny isn't.
In short:
Eowyn is very good vs heroes, but I don't think that's a problem at all as she is rather useless against everything else. And even against heroes she needs some levels to be really deadly (and leveling a hero in a normal game isn't as easy as you might think).
In case you think it is "unrealistic" for Eowyn to kill Gorthaur or the witchking:
Yes, in Terms of lore that would look rather strange, but as long as noone complains about a Hobbit beeing able to kill a Dragon by throwing stones st him I don't think we should talk about realism to much^^
I'm looking forwand to your response
best regardes,
Seleukos I.