I do know that if Voyager had done something similar and had Kes beg the Female Caretaker to save them from a Borg Armada, or something like that, no one would see it as anything but Deus Ex Machina.
Only if Kes had no relationship with the female Caretaker. Sisko had a relationship with the Prophets that had built up over five seasons, with them always asking something from him and giving nothing but cryptic answers back to him. In the wormhole, facing the Dominion fleet, Sisko had earned the help of gods and they finally did something for him.
If Kes had a similar storyline, then the writers could've gotten away with a similar resolution.
It's no different than how the TOS Enterprise could go anywhere at any speed and always had the right equipment or the right materials to make whatever they needed.
Starships always travel at the speed of plot. That's not a plot problem, and it's not a plot resolution. That's not what I was referring to. I recall Voyager
often solving the problems they faced by tinkering with the main deflector and shooting a particle-of-the-week at the anomaly-of-the-week, leading to a resolution of the story. Maybe it didn't happen as often as I recall, but my point is that the stories weren't often enough resolved by character choices, but by technological means. That's a valid way to end the story, but unfulfilling story-wise.