I have to mention how perfect 4e was for War of the Lance Dragonlance. No healing magic? No gods? Ok, no Heal or Religion rituals, no divine classes. That's it. Game still works perfectly without complex cascading mechanical adjustments. It's the only edition of D&D where Age of Despair or early War of the Lance works flawlessly.
To be fair though, you were never supposed to be without a cleric in DL. You would be without higher level clerical help - so, if you died, well, there wasn't anyone out there that could do anything about that. Your cleric in your group was likely the highest, or one of the highest, level clerics in the setting. Which still works in 5e. You can't go out and get a raise dead anymore because, well, there aren't any clerics high enough level to do that. But, you were always presumed to have a cleric in your group right from the start (or at least, right after the very first adventure

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Now, if you wanted to actually play in the Age of Despair? Sure, that would be tricky. But, there was never an assumption that you would do that.
And, let's be honest here, WotC is not going to expand on the setting either. It's going to be War of the Lance Krynn and that will be the end of it, same as pretty much any other setting that isn't Forgotten Realms. Which is fine. I honestly think the days where groups would play year after year in the same setting has largely fallen by the wayside. The rise of the Adventure Path has largely seen the end of that.
I do wonder if that fixes the cataclysm but hurts the aftermath... why did the faith break? why did it go so long without priests and why or how did the gold discs bring it back...
Part of it could simply be the loss of knowledge. People just didn't have anyone to teach them the rituals and whatnot for accessing clerical magic. Makes clerics a bit more like wizards, but, it also does make sense. Your regular D&D cleric is typically presumed to have learned how to be a cleric from other clerics of the faith. So, the whole "spontaneous holy person", while totally possible, isn't generally the presumed way that you become a cleric or a paladin.
And, there's the other side that with the gods gone, maybe clerical magic doesn't work. While it's not that the gods grant spells directly, but, clerics have a way to tap into the divine of each deity. With the deities no long available, the rituals stop working. Which also kinda explains why the gods didn't just turn off the magic - the only way to do that would be to up and leave, which would leave the world in the hands of the evil gods.