Yeah, I've wondered the same thing.
I saw another omegaverse manga where a God created omegas to be able to give birth to beastmen, and the beastmen were rare and treated as nobility (omegas were basically treated as breeding stock though - not much new there).
Anyway, that comic seemed to cover the "why" of the omegaverse (at least for its OWN story)
well, it's yaoi for a reason.
"As I understood it, it was an evolutionary response to a lack of women. "
No that is not the general gist of it. I've not met one manga that explained it that way. Most of them explained it that alphas, omegas and betas are just how it is from the past, not because of any evolution. For example, it existed from the creation of humans. It's not something that cropped out from a need, the earth was simply born that way from the start(in most if not all mangas).
I've met fanfiction that has said it that way tho. Omegas and alphas are just creations an AU(alternate universe) where fans/writers/artists can get the boys pregnant or they like the alpha/omega dynamic. Fated partners as such. There are also such things as omega females and alpha females. It is not only for males.
So 'evolutionary response to lack of a woman' might have been ONE author's reason for alphas and omegas but you should not use the idea for all mangas you read, not everyone has the same thinking and it seems most generally do not have that thinking.
What I read was somewhat unclear as to origin but did imply an evolutionary response to a crisis. It also seemed that in "pure" (I'm not sure how to term it) omegaverse, while there were some with outer female characteristics and others had more male appearance, the importance was the plumbing, so to speak. The difference between genders in omegaverse being less, as most had a womb and penis, though the "females" were able to get pregnant and their penises smaller. But I wouldn't be surprised to find out that that's all wrong.
Maybe we can all agree omegaverse is a way to wrap one's head around different sexual orientation and get us less focused on the gender binary we were most likely brought up in by having everyone having a chance at babies. When they say two omegas can't have babies (one I read said that,) we can think of it as a couple who is sterile but still chooses to be with the one they love. There was one I read where an alpha became pregnant. It is all up to the author's interpretation of the rules but each pairing shows a sign of struggle, whether physically or socially.
Are there any manga with female alpha x omega as the main characters (Sex Pistols has some but not really lead characters) or Alpha fem and omega male? There's some fan fiction yuri (I am not interested in yuri though if it's omegaverse it'd be interesting). And also wondered if a key choice of omegaverse would make it easier for fans to find new ones.

Well, I think that the alpha will soon discover that life is what happens while you're making other plans.
But I still wonder at the logic of this kind of omegaverse. If women exist why would omegas (and the rest) even evolve? As I understood it, it was an evolutionary response to a lack of women. Or have I seriously misunderstood something?