Again, the reader is assumed to have played the game, so they know that the description ascribed to Phoenix does not fit the the Phoenix (rebirth and hope) and instead they ascribe a description that fits Ascians instead (which the reader should also have knowledge of because reading this assumes you have played the game).

And you are the one being reductive because you fail to take the conclusion one step further and not use your knowledge of Phoenix from the game.
It should really go without saying that the behavior of the bird in relation to the modern idea of the phoenix is not even close to the only dynamic at play and the story and I'd argue it's certainly not among the most important comparisons we're meant to make. In fact if you want to connect it to the player's knowledge from the game, our experiences with phoenix-entities come from Louisoix and Suzaku - The former a man who was once considered a hero, but drew upon the power of a primal and became tempered, losing faith in mankind, and the latter trapped in eternal grief for the loved one she'd lost, wishing for the power to bring him back and cursing you for not living up to him.

A false hope. 'Tis folly to place one's faith in so flawed a race. "Stand together"? Hmph. They would first need to agree on which direction to face. If history teaches us anything, it is that man cannot find common ground between his own two feet.
And you! You dare think yourself his equal? His better!? Then I will put you to the proof. And when you fall, it will be a fate most deserved.
The parallels between these characters in these situations and Emet should be obvious. If you want to focus on the phoenix as seen through the player's experiences in-game, that just further deepens these themes tying back to Emet even more. In every circumstance with a "phoenix" thus far, "rebirth and hope" is in fact something someone else must bring to the phoenix, first Emet to the bird, then WoL to Louisoix, Suzaku, and Emet himself. I hadn't considered these connections previously, but now they seem as intentional as can be considering the storyline.