The problem is the Celestials tend to be big and strong entities while the demons and devils have more grunts. I can't imagine an army of Solars flying into the local hills to smite the evil kobolds and goblins.
Why not? Seemingly, it is easy to imagine an army of demons or devils sweeping into the local village to smite the village priest, lay waste to the town, slay all the local monks, etc. In RPG stories stamped from a certain mold, this sort of thing happens all the time.
So more likely they would work as the village hedge wizard/witch keeping evil at bay covertly. And I have used this trope in my games from time to time and probably in equal proportion to the evil witch/hag/devil encouraging vileness in the village covertly.
I'm more ok with that than the typical usage provided by D&D. However, I'd be interested in how many published modules had an explicit celestial working as an ally with the PC's (covertly or overtly) to counter the vileness covertly encouraged by the bad guys.
So, I don't understand. Why not, angels? That question is on you. Why don't you use angels?
Mostly gamist reasons. They deprotagonize the PC's. Any time you have a truly powerful NPC that threatens to steal the spotlight from the PC's its a potential problem. A world that regularly had active celestials would be one that was less dependent on mortal heroes, and this makes the game less fun.
Since I don't run an overtly gamist game, then it becomes necessary to find a simulation reason explaining the passivity of the immortal forces of good in a way that allows them to retain their objective goodness. The logical explanation is that both evil and good have some sort of truce in play because open warfare between them would result in an outcome neither side desired. This results in a world where both the immortal good and the immortal evil act in ways that are subtle and covert, and where the chief impact of both is through mortal agents (spells, for example).
Last time I ran an invasion it was from an alien LE plane (not Hell). I've always wanted to have a modron invasion but haven't gotten around to it. Yes, the party would be fighting being of pure LAW trying to turn the prime material plane into a world of clockwork lawfulness.
Which is cool, but doesn't really address the question. If 'law' invades the world, why doesn't 'chaos' counter-invade to prevent law from achieving this objective?
Because if celestials are busy chatting you up, then there are two parties of infernals doing whatever they want while both you and celestials are having tea.
That doesn't follow. This is like saying while the infernals are busy contracting for the souls of wizards, there are two parties of celestials doing whatever they want. There is absolutely no reason to assume the celestials need to be wasting their time assisting mortals. What I mean is, "Why don't celestials frequently pop in in the middle of adventures and say, "I notice you are low on hit points. Mind if I lend a hand to prevent a TPK?"", or else why is it that when you are tracking down the evil cult, you don't get to the headquarters to find a group of Archons cleaning their swords and saying, "We were just finishing up here, but good effort."", or else why don't you have celestials popping in to say, "Mind you don't overlook this important clue.", or simply, "The Grand Vizar did it." The reason that this is important is that you do find the opposite, infernals popping in to lend the bad guys a hand, or heroes going to the good headquarters only to find the good guys have been massacred at the hands of infernals. Why is it that only the infernals seem to find a way to make themselves useful? In point of fact, the only time celestials show up in a fantasy story is so they can be revealed as fallen celestials latter. Fallen celestials are apparantly far more common than the unfallen sort, which at the very least suggests to me an incoherent cosmology, and in point of fact is probably more closely related to the problem of any promenently featured paladin is certain to fall sooner or latter.
IOW, there's no reason for the celestials to track the party down (or to attract the party's attention) assuming a modicum of heroism on the party's part.
Then why is there a reason to assume the infernals track the BBEG down, assuming a modicum of villain on the evil cult's part?
Evil doesn't want to sweep mortals away. They want to corrupt them. Can't corrupt the non-existent.
Sure, but if you first sweep away all the sorts that aren't easily corrupted, then it makes it alot easier to intimidate, corrupt, and control the rest.
But the biggest problem with this statement as a rebuttal is that traditionally D&D doesn't portray infernals as subtle corrupters and their role as such in traditional D&D is very minimal. The traditional usage of D&D infernals and the role that they are statted out to fit is of combat centered monsters, differentiated only by flavor and not by mode of action from any of the other monsters in the book. So if you really wanted to focus on infernals as corrupters, tempters, and decievers you'd probably be motivated to not use the traditional D&D demons or devils at all, since, as you point out, mostly they are grunt monsters - the equivalent of high level orcs and are typically employed as such.