I’ve been thinking this *exact* same thing lately. While she didn’t have it when we last saw her, it honestly wouldn’t shock me if she had gained the Echo when we next see her. It’s hard for me to explain my full reasoning for this, but I’ll try.
A few things first. Alisaie is more of a ‘fighter’ then her brother. At the least, she dislikes dealing with politics, in contrast to him. To quote Alphinaud:
“And as you never fail to remind me of my fondness for diplomacy, I feel it only right that I remind you of your aversion to it.”
At the end of the Binding Coil storyline, Alisaie states:
“I mean to find my own reason to fight for Eorzea.
And when I do, I will fight with all my being.
You have done so much for me, Forename. One day, I hope to be able to repay you in kind.
I have no doubt but that you will continue to help those in need, and grow ever stronger in so doing.
I shall endeavor to do the same. And if the Twelve are kind, I hope one day to become Eorzea's sword in the darkness─as you are.”
And finally, at the end of Binding Coil Turn 12, it’s implied Louisoix gave the twins the potential to summon Phoenix-Egi.
Since Alphinaud gained a ‘power-up’ in the form of Onyx Carbuncle, I’ve been starting to predict that Alisaie will eventually gain her own power-up in the form of Phoenix-Egi.
There has been a lot of emphasis placed on the importance of the Echo, and how it marks ‘Haedelyn’s chosen.’ When Ysayle died, it was revealed others besides the Warrior of Light can gain Crystals of Light, and in extension some degree of the Blessing of Light. Though it’s implied the WoL is the first and only one to have gained six Crystals, which is part of what makes us so special. To quote one of the Ascians at the end of Haukke Manor:
“It is no ordinary mortal who can acquire one Crystal of Light...much less three.
The crystals make you strong, and it is to that strength that the Light is drawn.”
Furthermore, it’s been repeatedly stated that while the twins have ‘different paths’, they ‘share the same destination.’ In other words, there’s been significant foreshadowing that Alisaie will come to play a much bigger role in the main plot then she currently does. To quote Alphinaud during the ‘Another Turn in the Coil’ quest:
“My sister must needs have a better reason to fight. A time will come when the fate of the realm rests upon our shoulders, and when it does, we must be strong in our resolve─and certain of the stakes for which we risk all.”
So, we have Alisaie just waiting for a reason to Jump at the Call, and foreshadowing that she will come to play a bigger role...And what better way to fulfill both these things then by gaining the Echo? Giving her both her badly needed reason to fight, and immediately elevating her importance in the grand scheme of things. I’m even going to go one step further, and predict she has/is going to gain her own Crystal of Light, even.
As far-fetched as it may sound to others, Alisaie may have learned of the danger via Haedalyn/the Echo. That would possibly explain a lot (including why no one sans the merchant reported seeing her, despite confirmation she was in Vesper Bay and thus in the vicinity of the Waking Sands).