I always thought that as the omegaverse takes some inspiration from animals packs and that stuff, that the fact that omegas are more homely was mainly because in the animal world the females are the one that USUALLY deal with that stuff.
And regarding the housewife thing, is mostly due to a cultural thing. Remember that Japan is still quite a patriarchal country so I don't expect them to have the notion of a "househusband (?)". What I did like is that Hikari never addressed Masaki as Mum, mother or any of the sorts.
Omegaverse is a fantastical world in which, among other things, men can be impregnated and reproduce (which isn't a thing in Japan or any other country, as far as I know). It shouldn't be such a stretch to simply call characters what they are when a romantic partner is a) the primary care giver who b) identifies as a man and c) is married. It's there on the page. I'm well aware of how culture influences societies, and the obvious inspiration for the alpha/omega mthos. My issue is how frustrating it is to see how far omegaverse world building pushes against tradition and still retains some of its ugliest aspects. It's an unpleasant dissonance, for me.
Anyhoo, house husbands exist in Japan: in small numbers but they are more than a "notion". Japan isn't nearly as monolithic as we like to think.
Besides the more obvious stuff, what annoys me the most with omegaverse stories is the weird bits of gender essentialism it retains in what ought to be a more gender fluid world. We have male characters who identify as men and yet still have to be called a "house wife" and a "Mum" simply because they are primary caregiver. Would it really be mindblowing to have house husband and two Dads? It's not women's work by definition.
Anyhoo, Hikari chan and the fam charmed into reading it all, despite myself. I have two younger relatives staying with me for the summer; it was fun to compare mannerisms (▰˘◡˘▰).