Well, hilariously the Fallout games actually show why this likely wouldnt work.

Many of the Vaults had one kind or another of societal collapse/revolt within the Vault for many reasons.

Like, if you are in Zuck’s doomsday compound as a security guard… and… money doesnt mean anything any more because the world collapsed… and you can just shoot him and stop following all his insane demands… why wouldnt you?

This kind of thing is also pretty common around the world and throughout history when money kind of stops working.

Ultimately it all comes down to having a functioning society that can afford to have specialized labor roles. They’ll run out of food stores eventually and have to go outside and farm.

Which means farmers, security, you know a society with roles and values and ideologies that convince people its worth continuing on this way…

Its basically imposible to predict anything other than uncertainty and chaos when a shock or collapse of significant magnitude occurs. You could be right! But also possibly not.