Actually is a common thing in omegaverse that everyone could carry a child... that's why, even people with prejudices against omegas can continue their lineage. At first, the most common plot in omegaverse was that alphas refused to marry or pair an omega because they were seen as sluts and an obstacle in their carreers, or pair only as a mistress to bear children when they already had a wife. It was really painful and nerve-wrecking to read
And some versions have it that it's harder for alpha x alpha to conceive but the best chance is alpha x omega - hence being seen as a desirable child-carrying spouse for alpha families - while others don't have that aspect, which makes alpha x alpha the most desirable pairing for the elite families.

Wait, i'm lost...
Since when alpha can get pregnant?!??