Most of the thin-skinned omegas packed up their shame and moved to the capitol wasteland, where irritated locals are reported to be killing them in droves with nothing but dart guns and persistence.
lolol no, but seriously, what zegh said. Omega deathclaws don't seem to exist. The packs seem to function as a sort of nightmarish but all-inclusive commune, with the close quarters habitation and the carrion left around their caves for the picking suggesting that they exhibit a cooperative spirit and and a dedication to each other as individuals and as a pack that surpasses that of most pack mammals and even humans. As genetically perfected death engines, I'd imagine everything possible was done in their creation to eliminate the sort of physical deficiencies or confidence issues that lead to alpha/omega posturing, leaving instead a fierce "esprit du corps" and a strong loyalty to the commanding figures of the pack.
Physically speaking, it's possible (I'd say likely) that the runtier deathclaws lack the strength to break through their tough egg casings and die in ovum, or that they're weeded out young, but that's just conjecture. It's entirely possible that the lone deathclaws you encounter throughout the games are outcasts from their packs, too, meaning I just wasted a bunch of words on nothing. Tellingly, though, the ones in Fallout 2 who had their intelligence bumped up to (barely) sapient levels revered the one clear physical Omega of the species we've yet seen, Goris, for his wisdom and intelligence, and though he often went his own way he was always welcomed and cared for like any other member of the pack.