Some feel its inauthentic and trying to cheat the system. I generally feel its a fine approach. Whatcha gonna do?
Say something like "I'm okay with it, but other people might not be." instead of talking in circles trying to cover every possible answer every possible person may have
Yet you presented that as the binary options.
Disallowing anything happening in response to the prayer is easy. Allowing it opens up all sorts of nonbinary options of how to resolve the attempt, to what effect (stabilizing, a couple hp, a full heal), what cost, is it repeatable, who answers, how does it manifest.
That could have something to do with how disallowing it stops the conversation ("No" is pretty final) and allowing it leads to details.
But I'll note the OP never asked "and how many hp do they recover?" It was was far more "Do you allow it, if it is a skill, what is the DC?" But I don't think anyone expects us to have all the little details worked out. We don't need to discuss which god answers, because that is impossible to decide without first deciding which gods exist.
One thing I will address is that it seems like the repeatable aspect is a major sticking point for some people, and a lot of the other side have been confused on why it is even an issue. One time miracles are a pretty common trope, there is no reason to disallow this simply because you don't want it to be repeated.
I am saying there are multiple valid options that lead to different game experiences that can be fun game experiences. I am not advocating that any of them is the way things should be. I am against one true wayism.
I have my preferred option which I stated in my first response in this thread, but I think others are reasonable and can be within the normal parameters of the freedom that D&D gives on how D&D worlds work.
Your One True Balance is noted, but no one in this entire thread is going for a One True Wayism, and frankly the implication is a little insulting. You gave your answer, and I said "cool".
What is annoying me is you are treating this like some deep mystery, some unknowable problem. Like, if the OP had asked, "My fighter saw the Five Armies movie and wants to shoot his sword with a bow like Legolas did, how would you adjudicate that? Would you allow it?" And you just keep repeating "There are many ways you could go, and they are all valid options"
Yeah, we get that. That's why it is a question worth asking. If there was only one possible answer, like for example if the question was "My fighter wants to attack an enemy with their sword, what do I do?" then most DMs wouldn't even bother asking. Stating the obvious doesn't help us have the discussion. Yes, many DMs will rule in many various ways. We get that. We've been in these discussions before. That doesn't tell us anything.
Because I believe we are talking about D&D and D&D is open to a lot of options that involve a lot of consideration. Again I am not advocating that one way is best. I legitimately feel there are multiple fun valid different ways to approach this stuff in the game.
I have never claimed that one way is best either. You can step down from your podium now, we all know that everyone's way is valid and no one has the best answer.
That doesn't mean we can't advocate for our favorite options. That doesn't mean we can't discuss the options. I legitmately feel that discussion would be more interesting than just repeating the facts we already know.
I have not gotten the same impression of Eberron stuff that you have.
Eberron clerics seem to be a magical spellcasting tradition that taps divine power. I don't read it as belief powering clerics.
From the 3.5
Eberron Campaign Setting book pages 34-35 on clerics as a class.
"Other clerics across Eberron serve no church and claim no allegiance to any deity. They recognize the power of the deities, but not their authority over mortal life. They hold principles of alignment or other abstract ideals higher than the deities who claim these ideals in their portfolios, and
they draw divine power from the pervasive spiritual force in the world instead of channeling it through deities. These clerics are usually outcasts and loners, but the reality of their power is impossible to deny, and it lends credence to their unorthodox theology."
I don't take that as belief powering divine magic here, rather just not getting power from a god.
I don't expect Eberron non-clerics to pray and get cleric equivalent magical effects. Do you know of examples where people with straight up faith do stuff without say the trained spellcasting tradition of clerics or a specific feat? Clerics can clearly believe most anything and still do cleric stuff, but that seems more consistent with the class and not the belief being the operating factor.
Also there is the whole discussion about corrupt clerics keeping their powers on pages 35-36.
"A cleric who violates the tenets of her church or deity might risk punishment at the hands of the church (though not necessarily, particularly in regions where the church is very corrupt), but risks no loss of spells or class features and need not atone. This rule supersedes the information under Ex-Clerics on page 33 of the Player’s Handbook."
This seems to suggest that clerics who don't believe but are putting on a mummery of faith would still cast clerical magic.
I do like that
Faiths of Eberron says up front that "This book presents religious information through the eyes of believers, often stating as fact events that more properly belong in myth or legend."
I have not read a ton of Eberron. I have skimmed a bunch and like a lot of it, and played in the setting and adopted a bunch of elements into my homebrew setting, but most of my knowledge is high vantage point stuff. The stuff I have read though gives me a different sense than you seem to have on belief and magical effects in the system.
I am open to seeing specifics that point a different direction though if you can point them out.
I'm running late for work, so I can't go into my books with deep detail. The 5e books present a lot of similar ideas, but there are a few things specifically that stood out to me.
The Undying Court is explicitly said to be powered by their followers. The faith and love of the elves for their ancestors is what gives those ancestors the power to act on a god-like status.
The Thrane, home of the Silver Flame, is said to have the greatest number of paladins and clerics because of the deep faith of the populace.
As for specific examples, in Exploring Eberron Baker's 3rd party supplement for 5e, he talks about a common legend on pg 51 about an old smith who claimed Dol Arrah and Boldrei empowered him to smite down bandits who attacked his village, then died soon after. He also says that any player character with faith could temporarily receive a boon tied to a specific purpose or quest, then lose that power when the quest is complete.
Reading through another section quickly, this book is where I feel it is spelled out the most clearly. So, Kanon I guess.