That's a fair point, I've mostly been coming at this from a game play/content angle. Story wise I agree it's more wrapped up than other Primals. I guess in terms of pure lore you can argue that Phoenix and Demi-Phoenix are not one and the same, just like the Egi and the Primals are not one and the same. To be able to summon an Egi of a specific Primal all a Summoner has to do is attune to that Primal's aether. You could argue this attunement was already achieved during the Coil events, or like when the Summoner tries to call forth Ramuh Egi, we go to where it's remnant aether is most potent.

So for me it seems there's already things in place to give Phoenix to SMN without bringing him back into the main story anyways.