I think it would depend? In a lot of omegaverse, betas are the majority (I think 70% of the population is the usual rate), and it's not like beta men can produce children. In that case, that sort of thinking would be normal and would likely be the prevail ing view. Our characters do have secondary genders, but they live in a society like ours, so it makes sense why the MC thinks that way.
Also, in some omegaverse (though I'm not sure if this manga is one), male omegas can't conceive as easily as female omegas. For a family that needs heirs, the idea that a man should be with a woman would probably still exist, for the ease of having a child if nothing else.
I think a lot of authors forget that if the world was always an omegaverse, the idea of "men and women" should be together wouldn't exist; it would be "alphas and omegas" should be together. (Actually it goes deeper than that, but that's wll that's relevant for now.)