I don't think that damage is the issue here. To me, it's what they represent. And I'm not talking about their power-level.
Just look at Chaos Lords, pretty sure that everyone knows what they are. To me:
One of the strongest characters in the game (let's see how that can be made without being overpowered or turn to hero-hammer).
Can take a hit, and still go on (defense!).
Strong duelists (not the best, but probably at the top 5 generic characters, and can push back some named ones).
Not specialized in buffing their army, more about intimidation and brute force than anything.
Has some chaos-flavour (mainly chaos marks, but probably artifacts, traits, mutations, etc...).
Slow on foot.
Can turn in to spawn or Daemon Prince! (Eye of the Gods).
...probably more, but you get the point...
That list is what you have in your mind for each of your heroes. What are they, why you paint them with this scheme, the main reason to convert them and maybe even why you started their army. Their rules (warscroll and battle traits) should have all of this represented in some form. If there is a lot missing in their rules, this heroes becomes just tokens that you take because they have an ability that you want for your strategy. To me, that's shoudn't happen.