I'm not nominating taking the regular cleric out or replacing them or anything. *every* party needs a healer and a buffer. It's an essential and vital (if not very showy) role, and the cleric does wonders at it.
What I am saying is that it may not be a bad idea to distance "religious figure" from "healer." They don't have to be the same thing.
I'm not saying the cleric is a bad class, I'm saying that it's mechanics (as a healer) have baggage that it's flavor (a religious figure) doesn't nessecarily entail. And that's where the desire for specialty priests comes from, methinks. You think it'd be cool to play a character who worships a war god, for instance. And then you have a cleric with baggage.
The cleric works great as it is, don't get me wrong. I love that is has any versatility at all.

I'm not saying get rid of the healer. I am saying that there is a niche for a focused religious type without the baggage of also being the healer, because it can be superfluous to the character concept.
The designed specialty class certainly doesn't replace any other one. I mean, I'm not Fantabulous Rules Maestro, but I know well enough that no one who is not a fighter should be as good a fighter as a fighter.

Ditto for others. The abilities that the class could gain that would mimic other class's powers are, as a rule, weaker than the powers that a class would get.
If you play a cleric that's been handicapped in some essential way (like in healing), you are forcing someone else to pick up that role. In essence, you have two clerics, one of which does all the essential healing roles and the other of which can't heal, and can't do much else vastly different or better than the other cleric, either.
If I'm going to make someone else pick up the healer, I may as well not be a cleric, even if it does fit my character idea as a religious archetype.
The class doesn't in any way replace or invalidate the need for a healer in the party. That's not a niche the specialty priest should be expected to fullfill. It does allow you to focus on what your character believes in and gain power from that, which may not fill one of the Classic Four Roles, but does fullfill the desire for a focused religious figure without forcing you to be a bad cleric in the process.
I think a lot of this problem could have simply been solved had the designers of 3e renamed the cleric "the healer" and given them less versatility and more buff/healing punch. Don't get me wrong, I love the versatility of the 3e cleric, but it's too much jammed into one tiny space. It's a healer, and it gains powers from the gods. These two don't have to be one in the same thing, and it results in a lot of healers with a bit o' baggage and a lot of people who gain powers from the gods with a lot o' baggage.
IMC, I've ditched the cleric in favor of this new class, and a class that focuses on healing (the white magician from FFd20). Two classes, one of which fullfills the need for healers, while the other one fullfills the desire for PC's who gain power from the gods.
I wouldn't recommend that universally (my current world has very very distant divinities, so this magic-lite class works well for the feel, and since the white mage uses arcane magic, it doesn't have to hail from the gods), but it does demonstrate a fairly minor flavor problem with the cleric...it tries to be both the reception of any and all religions, forces, and philosophies, and at the same time to be the healer. The two are not incompatable, but they are rather uncomfortable bedfellows.