What is "this kind of situation"?
If I have a setting in which the gods do not interfere in such manner, and there's a reason for that, and that fact is woven into its history, to violate that is incoherent. Literally. As in, it is inconsistent with the established fiction. The whole is no longer sticking together. Not cohering. Incoherent.
Similarly, if you are playing in a game set in the Old West, sans supernatural elements, an action declaration of "I teleport three miles out of town to beat the bandits to the Double-Q Ranch," ought to be a non-starter.
If there are literally no bounds on action declaration, you don't have "tactical infinity". You have Calvinball. Tactics is the art of succeeding using the rules and bounds of a situation.
I'm using "In this situation" for the default myth, tropes, and milieu of modern, out-of-the-box D&D. I'm assuming that orientation to setting because that is normative here (and surely because I know that is
@pemerton 's orientation to D&D; Greyhawk or 4e's Points of Light). That world is filled with miracles and magic and legend. The idea that a mythical hero crying out for their ally's life to some god (the god of either PC) to spare them and having a moment of grace afforded to them doesn't seem like a stretch to me...it seems right in line. If something like this never happened in the oratory legends of such a place infused with magic and miracles....no Joan of Arc or spontaneous conversions and miracles...just deaf ears and turned eyes by the gods upon all laity saddled with crisis forever...then I would think it particularly odd and sanitized and stifling in its odd rigidity (stifling both for players and stifling for the laity in their belief...no one ever cried out for the life of their child/friend/lover to a god in a moment of grave consequence?). It just seems like a sterile world of LOLMIRACLES governed by the artifice of a class-based system.
However...
* If you're running some kind of alternative like Dark Sun where the myth, tropes, and milieu deviate from the default of modern D&D? Yeah, I would feel differently about this sort of action declaration.
* If the action declaration causes the game engine to buckle? Yeah, I would feel differently about this sort of action declaration.
* If the action declaration is particularly injurious to archetype because of just how potent it is? Yeah, I would feel differently about this sort of action declaration.
But none of those 3 are in play for the default, high fantasy of modern D&D (here I'm pointing at 4e and 5e in particular).
Let me sort of wander through other D&D and see how I feel about this action declaration:
TORCHBEARER (as grim and dark and unforgiving a setting as there can be) - We're in a Kill Conflict and we're at the post-conflict Compromise stage. Given what transpired with party Disposition during the Conflict and Order of Might (meaning, the creature(s) had more Might than the PCs), I have to take the life of at least 1 PC. Lets say I go with 2 of 3 PCs and the 3rd one comes out with only a minor Condition. This can go three ways as I see it:
1) The players beg off of this and see if they can all 3 come out of this alive but with the Injured Condition (a grave condition that puts all 3 on death's doorstep and apt to cross it). We could skin that fiction however we'd like. Perhaps the Valkyrie comes to take them away and the remaining PC begs for the life of his friends...the the Valkyrie refuses but the friend grabs onto the legs of her friends as the Valkyrie begins to ride away, all 3 of them falling back to the earth. The fall breathes life into their breasts but they're all gravely injured.
We've reconfigured the Compensation and new fiction has arisen as a result.
2) The players could opt to spend their one-off Pay the Terrible Price (which lets them defy death but their Nature suffers terribly - Cap down 1 and they start back at 1/1, they are "changed" as they lose one of their descriptors and have a Trait altered, and the Nature change means they learn some terrible things, and gain insight, from the other side - due to the design of the Skill Advancement system, they would learn some Skills). We can skin this however we'd like including the remaining PC beseeching the Valkyrie through ceremony or force of will to release her friends, getting rebuffed, and she ultimately pulls the dead PCs from their place on the back of the Valkyrie's steed, reviving them.
3) After the Kill Conflict things are where they are, but the remaining PC wants to enact a (Last Man Standing) Spiritual Conflict with the Valkyrie when she is about to usher off her friends to the other side. The Valkyrie has Precedence on the PC so there is going to be a Compromise that the PC has to endure even if she wins. We set the stakes and goal going in and run through the Conflict. Maybe somehow the PC wins. It almost surely ends up exactly as (1) above but with a possible prospect of either (a) the PC that pulled them off being dead in their stead (and possibly Paying the Terrible Price - see 2...or riding with the Valkyrie to Valhalla) or (b) the PC that pulled them off merely being Exhausted (a terrible condition but not nearly as bad/dangerous as Injured) with the other two PCs being Injured (in a grave situation).
Whatever way its gone down...its awesome, we've learned a great deal about the PCs and the setting (the legendary few can rebuff or bargain with the Valkyrie though she, or the spiritual process of the bargain/rebuffing, will no doubt exact a grave toll), and it in no way causes the game engine to buckle under the weight of it (in fact, this is by-the-book handling within the game's engine).
DUNGEON WORLD/STONETOP - This would be interacting with the Death's Door mechanics. The only way I would let this happen in these games is the following preconditions:
1) The PC in question has a specific playbook move that lets them make a move to alter the fiction of the dead PC confronting the Black Gates/The Lady of Crows.
Failing that:
2) Their friend, still alive, is near enough to hold them and comfort them in their crossing over. They swear an oath to the dying PC that they will not cross alone. I would let the other PC "go with them" and they could take +1 for their Death's Door move with the living PC suffering the same consequence as the dying one as we confront The Reaper/The Lady of Crows. 6- and that is that. 7-9 and some profound concession/cost/oath must be made that binds the two PCs together and to the will of The Reaper/The Lady of Crows.
3) Their friend, still alive, is near enough to hold them and comfort them in their crossing over. They cry out "take me" or something of the like. The Reaper/Lady of Crows obliges...and that PC makes the Death's Door move instead, collapsing. We then find out what happens as the other PC draws a breath.
Same as above...doesn't break the game engine and something awesome has happened and new fiction has emerged around setting and characters (including significant risk/cost undertaken).
MOLDVAY BASIC - Not doing it, not entertaining it, and I can't imagine a player ever asking this. It would injure the game.
TLDR - Dark Sun or Moldvay (or some setting without miracles and magic and gods and legendary characters and mythology that must have some tale of this in their history) = No. Causes game engine to buckle = No. Is particularly injurious to archetype due to the potency of the effect w/ respect to the potency of the archetypal character's capabilities and/or well out of the order of what mundane stuff can resolve = No.
If none of those are in play = Yes w/ something sufficiently staked to create an interesting decision-point and a character-altering/defining moment.