It occurs to me, there's another very story-wise reason why clerics are not typically "battlefield" leaders, i.e. on the front line, except perhaps war priests. You don't want your cleric taking the first big hit from the cave troll, that's the fighter's job. The cleric should be more in the back, as a support role, not because "We're being mean to the poor old cleric class again"(tm), but because it simply makes tactical sense to do so. You protect the cleric, even more than you protect the wizard. Because if the cleric goes down, that's it folks, it's game over. Try keep going deeper into the dungeon now. You'll think twice, won't you? But that presupposes a more traditional "deadly" D&D which I prefer.
In a game where a simple 20 minute rest can allow anyone to go from being knocked out to full with 0 magic or even assistance (you could be solo, wake up in 20 minutes with no aid from anyone else in 4e, and be fully healed, without even a single skill or magic aid), I don't see how clerics or warlords or even any leader are needed at all to keep going, contrary to what you all said. But that's not a design flaw in the 4e cleric, it's a deliberate decision to make all healing non-magical, and "magic" is simply a fluff keyword. That is so wrong. I'd even still play 4e for fun if I can't find a decent PF group, but I don't see it as D&D. I see it as a tactics game. To make a healer -- whoever that is -- required to adventure deep into treacherous paths when all light has failed, which IMO I think it should be by default in D&D Next, you need to dial down the healing by default. On top of this, your party survivability chances should be at least 2x better, or at least no party member dead, per combat, with a cleric around.
I agree clerics historically never healed during combat, but this is D&D. It's supposed to be better than Tolkien or the Bible or Beowulf or all of them at modelling a workable set of adventuring classes, while still maintaining believability and risk of death. If there's no risk of death, why have a cleric? Why even play D&D at all? play a videogame.