It would, if that would have actually happened.
Not to drag the discussion too far away from the Enterprise but if we consider two episodes of DS9 with the Enterprise in them we can see some examples of the optimism of the show shining through.
1. Emissary (Enterprise D). Optimism of a whole new quadrant to explore. Optimistic view of Bajor rebuilding after the occupation. The optimism of building relations with a new species of aliens who live in the wormhole. Even the optimistic view that we can live peacefully across from our Cardassian neighbours.
2. Trials and tribble-ations (prime Enterprise). Optimism that Darvin can be stopped. Optimism that history will unfold the way it should. O’Brien optimistic that Bashir isn’t supposed to participate in a predestination paradox and become his own great great grandfather (because he still existed when they got back to Deep Space Nine). Good guys optimistic they will beat bad guys - in both centuries.
Now, zooming out to the rest of the series - we have:
The optimistic view that the wormhole is good for Bajor.
The view that the prophets will triumph over the pah wraiths.
The view that starfleet will defeat the dominion.
The view that Nog will get better after his injury.
The view that Worf will get better after Jadzia gets into StoVoKor.
There is never a sense of despair on DS9. Even in “the sound of her voice” the crew is optimistic that they will save the crashed captain.
DS9 illustrated the view that although it may be darkest before the dawn, we should remain optimistic that the dawn will indeed come.
Sisko’s speech to Worf about not resigning in “way of the warrior” encapsulates the optimism of DS9. And Sisko was talking about staying optimistic after the death of his wife.
YMMV of course, but Deep Space Nine was nothing if not optimistic.