You raise some very good points about Arena and are correct about EoM.
On the other hand, Sacrifice of Angels stood at the climax of drama that had been building for seasons. There was a great deal of investment in all of the nuances leading up to all out war between the Federation and the Dominion. DS9 had set itself out to be Star Trek's edgier cousin, and spent a lot of time trying to make the case that that's what it was. Also, because DS9 set itself up as being about story arcs, Sacrifice of Angels can't be separated from all the seasons of buildup and anticipation that had preceded it.
Then, as the great battle is about to begin, the show has this epiphany. After all those seasons, it's suddenly time to finally get back to its roots. Assuming we can cope with the whiplash of that, what do we get afterwards, in the remaining time the show runs? Total silliness, such as that involving the Pah-wraiths.
The problem wasn't that the theme turned out to be that war isn't such a good idea after all. That is consistent with the ideals generally associated with Star Trek.
By way of clarification, the problem was twofold. First, what little dramatic payoff we got was all out of proportion to the buildup. That's it being "poorly executed". Second, and moreover, it was all downhill from there, and yet the show meandered on for almost two more seasons. This, what I called jumping the shark, was the actual nature of my criticism.
While you raise a valid point, the fact is the Prophets have been part of DS9 since the beginning and never really left. It's not like the Temporal Cold War or the Kazons, where they dropped off the face of the Earth after a certain time period. The Wormhole that introduced the Dominion is the home, as well as direct conduit, to the Prophets. Indeed, the whole "we need to destroy the wormhole" plot which kept cropping up seemed horrific to me as this is the home of a peaceful race of aliens.
For me, the Dominion War was going to be a big epic darker and edgier story but it was never going to drop the Prophets arc. Those who wanted to keep the mysticism of the Prophets from their hard science war I felt were bound to be disappointed because that was as much a part of Deep Space Nine as anything else.
Since they needed to have the Dominion come through the wormhole, I pretty much wondered why it wasn't obvious from the beginning. "Can you [The Prophets] prevent this bunch of guys from coming through?" It seems an obvious question.
Oddly, my biggest problem with SOA wasn't that the Prophets COULD do this, it was the way they DID.
My problem with SOA wasn't that Sisko appealed to the Prophets, which is just fine, and then the Prophets straight up murdered (say, 1000 Jem'hadar on every ship), 3 million guys. That's a little disconcerting for Star Trek.
(And reversed by the video game)
I mean, it'd be more Star Trek if they'd just CLOSED the wormhole.