I'm confused. So teenage Alix just up-and-left her (semi-normal) life, friends, and family to go live in a space/time void?
Yes, apparently. It was to make sure that at no point Hawkmoth can get to the rabbit miraculous, because he's made a connection to it with the dog's ball.
Fortunately, the ball cannot pass through burrow directly, remember how Ladybug and Felix had to travel back in time to fetch the kid's doll? And when Felix used fetch in the present, the ball didn't travel to the past, it traveled to where Risk had hidden the doll in present time, meaning the Dog's ball cannot pass through the barriers of time. Even in Evolution, Gabriel threw the ball at Alix, she jumped into the Burrow, but the ball didn't follow her.
Both young and older Alix can never be in the same timeline as Gabriel, until they get Barkk back or until his defeat.
And since Hawkmoth still owns Barkk, if Marinette or Alix have the Rabbit Miraculous out in their homes or on their person outside the Burrow, he can still snatch it back. Alix's father was well aware of this, that's why they shared a goodbye, and that's why Chat said "Then Alix can come back." She's gonna hang out with her older self for now.
