I just posted a reply to another thread in this forum about this very thing.
In the real world, many people don't always try their hardest, even when they are trying to! That's why there are coaches. That's why people have personal bests that they can't always emulate. That's why people can be driven to do things for people they love that they would otherwise not have thought they could bring themselves to do.
The idea that everyone is entirely self-sufficient within him-/herself, and that feelings and relationships have no effect upon performance, is very atomistic. I think it's contrary to a lot of actual, lived human experience. And I also think it's contrary to a lot of the literary material that underlies the tropes and themes of fantasy RPGing. (The soldiers defending Gondor were trying hard. They were helped - tried harder than they otherwise would - because Gandalf went among them, heartening them and encouraging them. It's never occurred to me that the only explanation for this is that Gandalf is casting a spell on them! It seems to me that Tolkien is pointing to a perfectly commonplace aspect of human life.)
And the problem here is that you have to assume that everybody loves the Warlord or are heartened by the Warlord's presence, even when they just met the Warlord and have no idea who he is. I could have a Paladin fighting side-by-side with his deity, and he wouldn't feel inspired to fight harder until the Warlord (or Bard) decides to say a few encouraging words.