That scene is a triumph of Federation ideology.

Finding the wormhole was a lucky accident, but everything else which lead to that apparent deus ex machina came about from Starfleet doing exactly what was needed to get the Prophets on their side: not with the intention or expectation of that ultimate result, but because it slotted right in with what the Federation wants to do anyway.

Sicko and his crew communicate with these strange life forms in they find, and make an effort to not only understand them but respect their wishes. They offer enormous practical support to Bajor and attempt to encourage them to join the Federation formally, but they respect the wishes of the Bajorans even when highly inconvenient (such as the abrupt pivot away from Federation membership that preceded the Dominion War). In short, Sisko and the government backing him legitimately earned the trust of both Bajor and the Prophets by being explorers, diplomats, and excellent allies. The military payoff they got is hardly the point, but they earned it.

Would any of the other races have earned the favor of the Prophets the way the Federation did? The Klingons, Romulans, and obviously the Cardassians would have taken over as brutal occupiers if they felt the need to get involved with Bajor at all. The Ferengi would have ruthlessly exploited Bajoran resources in their own way (which we know the Prophets were no fans of, see their temporary rewiring of Grand Nagus Zek), while the Borg would have simply consumed everything they found useful. Here, it's the uniquely decent actions and values of the Federation that win out.