It sounds like you're assuming that Alien vs. Predator is supposed to be canon as far as Alien: Covenant is concerned, which doesn't appear to be the case.
In the last 20 seconds of this 2012 interview with Empire Magazine, the director of Prometheus and Alien: Covenant, Ridley Scott, states that he hadn't seen either of the Alien vs. Predator films at the time that interview was conducted (the same year Prometheus was released in theatres):
Empire Magazine: Just the very final question, because I've always wondered: Have you seen either of the Alien vs. Predator movies?
Ridley Scott: No.
Empire Magazine: They don't exist?
Ridley Scott: I couldn't do that. I couldn't quite take that step.
Judging by remarks he made during this 2019 interview with The Hollywood Reporter, it sounds like Scott was of the view that Alien vs. Predator had left the Alien franchise on life support, and that he needed to go back to the drawing board in order to revive it:
Ridley Scott: I think Alien vs. Predator was a daft idea. And I'm not sure it did very well or not, I don't know. But it somehow brought down the beast. And I said to them, 'Listen, you can resurrect this, but we have to go back to scratch and go to a prequel, if you like.'
And in this interview with CraveOnline, one of the screenwriters on Prometheus, Damon Lindelof, indicates that Scott wasn't interested in factoring the Charles Bishop Weyland character shown in the first Alien vs. Predator film into the Peter Weyland backstory they were creating for Prometheus:
CraveOnline: You said nothing is an accidental reference, so is there a possible intentional Alien Vs. Predator reference in that the Weylands are always seeking eternal life?
Damon Lindelof: You mean in terms of Charles Bishop Weyland? Look, as to what’s canon and what’s not canon, for me as a screenwriter it’s transcended by Ridley as a director. Here’s the thing. Ridley invented this. He created this Alien universe. He birthed it out of his own heart and soul. So he gets to do whatever it is he wants to do and he wanted to use Weyland as a conduit in the story, and was not interested at all when I said to him, “You know, Weyland was a character in one of the Alien Vs. Predator movies,” he just sort of looked at me like I had just slapped him in the face. That was the beginning, middle and end of all Alien Vs. Predator references in our story process.
In light of the above comments, it seems pretty clear that the events of Alien vs. Predator did not occur in the timeline Alien: Covenant exists in, which means that the Xenomorphs in those films could have very different backstories. The origins of the Xenomorphs and Alien Queen shown in Alien vs. Predator remain unknown, whereas in Prometheus and Alien: Covenant, it would appear that David is the creator of Xenomorphs, while Queens don't actually exist yet.
It also shouldn't be taken for granted that Queens will ever exist in the universe Scott has been building with his prequel series, since the Queen was something James Cameron came up with when he wrote Aliens. The writers of the first film intended for Xenomorph Eggs to be produced through the process of Eggmorphing (although this was only alluded to on-screen in the director's cut of Alien). Note that we saw a number of Eggs in Alien: Covenant, apparently produced without the need for a Queen.
Scott does seem to like Aliens though, judging by various remarks he's made about the film. So he might wish to incorporate the Queen into his prequel series, assuming any further installments are actually made. We'll have to wait and see on that front.