I also feel I have to digress a little bit into real world religion and its applicability to D&D campaign setting. Most people's take on D&D religion is what I call 'post-Christian'; that is, it is informed by a generic Judeo-Christian world view, but it in fact doesn't agree with actual Christian theology. It's a superficial take on it that you might have if you'd been to Sunday school when you were six or by osmosis from the general culture, but weren't yourself pious. Of course, you've every right to impose on the fantasy world any take on religion you prefer - generic post Judeo-Christian is as 'right' as Greek or Hindu in a sense - but from my part it does involve imposing some ideas that seem really odd to me in the context. Some examples:
I think that that's a fair and reasonably accurate description of my own approach.
I also think it's hardly surprising that it's a common take, given that the game world generally defaults to a pseudo–medieval Europe (complete with castles, knights, and princesses) that ditches the monotheism of the real world historical timeframe while not really taking into account the rather large societal impacts of monotheism in general and the specific doctrines of the dominant religion in particular, rather than using pre-Christian polytheistic societies as its basis.
2) One of the strangest things to me is the notion that the Cleric is some sort of 'D&Dism'. In truth, it's the Wizard that is the D&Dism. If you look at real world magical systems, almost all of them would in D&D fall into the sphere of divine magic. Almost all real world 'wizards' up until very near the end of the 19th century when magical systems based on science (or rather psuedo-science) started appearing are best classified in D&D terms as clerics. Almost most no historical magician believed that he himself works the magic, but instead believes that he influences some divine power or spirit into performing magic on his behalf. Almost no historical magical tradition believed it could perform the sort of flashy magic most closely associated with the D&D Wizard. Instead, the spell list would look a lot like some subset of the clerical list. If I was trying to recreate the world of antiquity as the ancients beleived it worked, it would be the Wizard I'd ban as a class, and all 'wizards' would be clerics of some sort.
You're conflating the Cleric in particular with the general explanation of magic as coming from divine sources. Divine spellcasting can be a more accurate representation of pre-modern beliefs about magic without it in any way altering the fact that the Cleric itself is a D&Dism.
To the extent that the D&D cleric is, in any respect, a model of a generic divine spellcaster, it's a shift from the original conception of the class, as well as the earliest published versions. The D&D Cleric of the original system isn't 'generic spellcaster whose magic comes from divine sources', it's an armoured warrior priest with an inherent knack for repelling the undead, who
also casts divine magic. At first level, they can't cast any magic at all.
As has been
recounted elsewhere, the original conception of the class had nothing to do with attempting to model a divine spellcaster. It was designed as a vampire hunter based on Peter Cushing's characters in the Hammer Dracula films to combat a specific player's evil vampire PC and his undead minions, then had healing and curing diseases added in, and then a weapon restriction based on stories about Archbishop Turpin.
3) In the D&D sense, Christianity has no clerics. The last Christian clerical tradition in the D&D sense died out with the Catholic counter-reformation in the 16th century. Christianity used to have Theurgists who cast spells and this used to be a somewhat approved method of interacting with the divine, but no longer. Instead of spellcasters, Christianity only believes in divine intervention now - miracles worked on behalf of the faithful often regardless of their clerigical caste.
In the D&D sense (at least the OD&D one), no religion has ever had Clerics. Or at least, none that I'm aware of. Perhaps there's a tradition out there somewhere of castle-building armoured warrior priests who fight undead while casting spells and eschewing the use of edged weaponry, and I've simply not heard of it.
4) In polytheism, it's really unusual to only worship a single diety nor is worshiping a variaty of gods generally seen requiring you to conform to a particular one or a betrayal of others. Yet it is a truism of D&D that just about every character has a single patron diety. It's polytheism, but its a polytheism where every diety is like a jealous Judeo-Christian God.
And a polytheism where the classes most closely tied to the divine are based upon Christian and post-Christian concepts (medieval warrior priest/1970's movie vampire hunter, medieval divinely inspired knight), rather than being based on any pre-Christian archetype (though admittedly at least a couple of Cleric spells are pre-Christian in inspiration, drawing upon the Old Testament rather than the New:
Sticks into Snakes and
Plague of Insects).
Sounds like meddling gods is a thing for you! I typically prefer a game where the gods are more distant. Meeting a god is like streets ahead of meeting the emperor, which is greater than meeting the king, which is greater than meeting the local baron, which is greater than meeting the mayor of your village, which is maybe something 1st level characters can do, if he's not too busy.
That might change, depending on the setting's other trappings, but generally if the mayor ain't gonna chip in to save somebody, sure as shoot a GOD ain't gonna do it.
My mayors are generally more active than usual as well, but there is a portion of your analogy that just doesn't work for me. Most of my mayors are like 50 year old 5th level Experts which no physical scores (STR, DEX, CON) above 9, no combat related feats, no combat related skills, often the Non-Combatant and Civilized traits, and no magical items related to offensive action. My mayors are generally comparitively to D&D tropes quite willing to help PC's in every way that they can provided the PC's present themselves as honorable persons, but really, what can such a character really do? Even when the PC are 1st level, they often have greater martial prowess than such a character. Beyond that, the mayors don't enjoy comparitive omniscience and omnipresence. They can't (for example) by concentrating see everything within five miles of every lit fire (per for example the 3e Dieties and Demigods), can't just pop in and help (per every editions Deities and Demigods), but must sludge through whatever obstacles that the PC's are facing to get to where they could help them, and mayors generally command no more than a dozen armed magistrates rather than legions of spiritual beings. It's not that the PC's haven't occassional recieved aid from such groups, because they have, but the aid they can offer is small and generally results in dead NPCs. Ultimately asking such NPCs for aid generally involves sacrificing NPCs to save the PCs, rather than the PC's shielding and protecting the NPCs. The same is not true of asking aid from the Gods. Arguably, many of the gods involved in the current campaign would rather the PCs ask them for aid than they ask the mayor.
The analogy doesn't work much for me either.
The local mayor generally isn't a figure of worship known for their vast power and benevolence, whereas Pelor (to again use the god mentioned in the scenario)
is. Pelor might be more distant than the mayor, but it's hard to reconcile a god whose teachings call for providing aid to those in need, but at the same time is themselves less likely to provide aid than the average mayor. It seems entirely reasonable to have a greater expectation of aid from the god than from the mayor, especially if it's widely known that the god
does grant healing (or at least the clerics of that god do, and claim that they get the ability from their god).
It might tax the limits of the mayor's abilities, resources, and schedule to provide aid ... but is a little bit of help even a minor inconvenience to a god worthy of veneration?
Though again, I prefer to let the dice land where they may, and then let the players decide for themselves whether their characters believe that a good result is evidence of the god's helping hand or simply random chance. Even in Greco-Roman myth, unambiguous manifestations and direct action are the exception (and generally an unhappy one for the people involved) rather than the rule: you perform a purifying ceremony at the temple of Apollo and your minor illness clears up a few days later ... did Apollo grant you your health, or did you just happen to get better? The typical person probably didn't expect to ever get Apollo making a personal housecall, or even an instant reversal of their condition upon completion of the ritual.