If you fluff it that way, why is it that an ultra-charismatic non-warlord can't accomplish the same task using raw natural ability? It's just so completely utterly arbitrary and gamist that only a warlord can do this. Inspiring people from death's door is NOT part of a profession. A father or loved one can do it, a close friend and comrade-in-arms, charismatic priest invoking your faith in a god (without healing magic per se), etc.
Well, anyone can activate a downed character's second wind, representing, as I see it, physically trying to get them on their feet and back in the fight. Outside of that... I'm sure there are skill and utility powers scattered across the place that would represent this. Outside of that... the Warlord is a natural born leader, the type that others follow into hell itself, and not everyone can lay claim to that sort of thing.
Sometimes the fallen will still find themselves able to get back in the fight (rolling a natural 20 on a death save and getting back up), and this can easily represent them finding something to inspire them back into the fight.