Is there an inherent problem with the Warlock being a Cleric with different mechanics?
I think it's a sound principle that different core classes have different identities, and that different mechanics represent different forms of power. If the warlock is simply a cleric that has a different casting system and list for no particular reason, then that's page space in the book that could be better spent on a more distinctive class. Fortunately, it's not.
That is basically how I view them, and have since the beginning.
I feel like that's a missed opportunity for you in exploring the differences -- and potential tensions -- between divine magic and pact magic. Let's take Asmodeus as an example, because he is well established in the core lore as a patron of both clerics and warlocks. What makes a cleric of Asmodeus a fundamentally different core class than a warlock? Well, a cleric has an ideological commitment to her patron. She's a true believer, on Team Asmodeus heart and soul. His goals are her goals. Her alignment is thus unlikely to stray far from Lawful Evil (although never say never under 5E alignment philosophy). This faith is the source of her power, what it means to be a cleric.
None of this is true of a warlock. A pact is an economic exchange. The warlock fulfills the terms of his contract not out of commitment to or belief in or affection for Asmodeus, but because Asmodeus is giving him the power he wants for his own purposes. In a strange way, he and Asmodeus almost negotiate as equals. Now, he might be an evil bastard and be amicable to Asmodeus' goals, but they're still not
his goals. And he might just as easily abhor everything Asmodeus stands for and actively oppose the archdevil's clergy wherever possible (although doing so openly enough to piss Ol' Ruby Rod off is of course dangerous for his health). So his alignment can be pretty much anything.
Isn't this just a bit more interesting than saying, "Well, the difference is that the warlock knows
eldritch blast and refreshes spell slots on a short rest"?
Cleric is actually at the top of my list for classes that need a full overhaul, because I find them bland.
I don't entirely disagree. But that's a mechanical problem, not a flavor problem. You can borrow mechanical tools like a limited quota of spells known from the warlock (and sorcerer, and bard...) in order to make individual clerics more distinctive, without giving up on their identity and just rolling them into another class.
And I will say as a counterpoint: how often have you actually played a cleric? Because in my experience, the 5E cleric always having its domain spells prepared has a surprisingly profound effect on how clerics of different domains approach adventures.
As far as "The problem", there are two ways to look at it. From a story point of view it's fine in the world, and the patrons clearly allow it. From a mechanics point of view, it is a problem, one that can be handled at the table level, just like the Hex+Bag-o-rats that everyone was up in arms about a short while back, and probably much longer before that.
I think there's a slight difference between setting up a bag-o'-rats exploit and simply saying "I cast this spell. Okay? Good. Then I short rest. Okay?" And you still haven't answered the question of why it should have to be handled at the table level. If an obvious exploit has to be handled at the table level, that is a rules failure. And since we're dealing with a
playtest document here, now would seem like the appropriate time to make sure the rules don't fail.