I don't think the Alien actually benefits from an AVP story as much as the Predators do. The Alien is typically played as this ultimate prize where the Hunter(s) have to kill one to be worth a damn. Except in an AVP story the Aliens are torn down rather easily and the films make it a note that the more experienced Predator has no trouble at all until it comes to the Hybrid or Queen.
To that end it means that the Alien has less to gain from the experience than the Predator does because it ultimately becomes fodder.
The Predator however greatly benefited from an expanded mythology which also included the ultimate hybrid between the two, the PredAlien. The Predators hunting Xenomorphs becomes as a result this manhood ritual in-universe. It also benefited from the symbolism of a boy becoming a man by metaphorically claiming his penis. The Alien being this symbol of unchecked male aggression and sexual violence is used to convey that that the boy has become a man, and that in slaying the dragon he has proven himself master of his domain. He has proven him worth the respect of peers. And because this is conveyed in the subsequent films it means that the Predators get to embellish themselves. Make no mistake, this is the underlying reason the Predators are even present in the original comic. You become a man by proving your dominance. And to that end I say that works astoundingly well for the franchise which is why it was never jettisoned even after Prometheus screwed the timeline up.
So what needs to happen in an AVP 3?
The Knight needs to slay the Dragon.
The Knight needs to come in on his white horse and save the princess from the Dragon.
In short what this film needs to do is simple, have one Predator and have one Alien. The Alien is a threat because it will takeover eventually given enough time and she can spread fast which creates obstacles for the Predator. Said obstacles can be metaphors for feats the Predator must perform to gain access to the Dragons's lair (the hive). Because they take traits of their host, they really can represent that. Be it the elements, or strength, speed, courage, etc. The Predator only has to come in and prove his worth to the Princess (the clan, the humans, or himself). The Predator (the Knight) then confronts the dragon and this battle then decides if he is worthy of his honor. Does he prove himself?
To that end AVP isn't about the humans, it's about the Predator. The Predator's story is the important part which serves as the narrative catalyst, and the means to its end.
AVP 3 does not have to be this all-inspiring epic nor does it have to be straight horror. AVP is at its core a knight slaying the dragon.