As Skaven in multiplayer, I noticed that once your LL is dead, the whole army routs within seconds even if the most of the units are on full HP. On the other hand, when you are Skaven and kill the Dwarf LL, they manage to play for 15 minutes and even defeat you in worst case. Not to mention Flying Lords who end up alone with some flying unit or hero who can easily pick off Skaven units (including ranged in late battle, when they are out of ammo), and win the game despite having a total disadvantage in numbers (remember, their army is wiped off and only Legendary Lord is alive with one or two flying units, while on the other hand Skaven has tons of units and LL alive).
So how come that killing a Skaven hero is almost an instant lose for him, while other factions can play the battle a lot longer without LL? In older Total War games, such as Rome Total War, killing a general at the start of the battle with a first halo of catapults equals a lost game for sure. Shouldn't the killing of Legendary Lord have harsher penalties on the whole army, not just for 60 seconds? And shouldn't these penalties be present for all factions? There should also be "severely outnumbered" trait that would inflict penalties on the army that has no land units and ends with a flying LL and/or a couple of flying units on the battlefield. Having said that, I noticed that the armies that remain with only flying units can actually fight and even win despite the fact that there is an actual penalty for the army that ends up with flying units only on the battlefield.
Anyways, I think that Legendary Lords and Heros should have "wounded" trait the lower their HP is that would reduce their ability to fight properly. Their leadership aura should be reduced as well as their morale. Cooldown for LL's abilities should then be increased. In the end, if killing a Skaven LL is a GG, it should be the same for every race out there. You either fix all of this or give Skaven flying units and LL so that they can exploit already broken in-game mechanic for other races. So in the end, killing a LL should be an instant rout of the whole army for , or the army's ability to fight should be affected for 5 or 10 minutes.