Bro, not everyone got into the Vaults. There are what, over 300 million people in America? Probably way more in Fallout universe considering it was 2077. The Vaults only held about 100,000 people (no, not each Vault. All of them together). That's still 299.9 million people left to face the bombs, or in 2077, I'd predict about 499.9 million though some websites predict America alone will hold a billion people by 2080.
When your walking around in New Vegas, on the outskirts of the strip, you don't see all those houses boarded up for no particular reason. "Hey, before we leave to the Vault, let's board up our house. Maybe our shit will still be here when we get back... just in case". Not trying to be a dick, I'm just pointing out the fact that less than 1% of the US population got to have a place in a Vault. Each Vault only held 1000 people (granted, some Vaults may have been bigger, but no bigger than about 2000 most people suspect). In 2080, "small" US cities will hold at least a million citizens. There were what, 120, 130 Vaults commissioned. Giving the Vaults the benefit of the doubt, saying that they each could hold at least 1,500 people, that's still only 180,000 to 195,000 people. Even if we say America had a horrible birth rate, our population would grow at least 50 million by 2080. That's 350 million people in the United States, and 195,000 (taking the bigger number) able to have a position in Vaults.
And in this scenario, it's not "breaking into a random person's house". In any kind of disaster scenario, for most people, survival instincts take over. When people rely on survival instincts alone, its chaos. The United States has never really faced a "great" disaster scenario since the 1920's. Look at the LA riots. Detroit riots. Weren't even really that bad in comparison to something like a world wide nuclear war, or a world wide deadly flu pandemic. Yet look how people acted. Also, look at 9/11. The people in those towers who jumped? Survival instincts took over. They knew it was be burned alive trying to wait for rescue, or have your death be instant. Most the time human's aren't even thinking rationally during disasters. They've let their mind be completely taken over by their own human instincts, and it's almost like they are being ran by their subconscious. It's kind of like how, when say something happens such as a burglar breaking in, someone's instincts immediately take over, and they do something like bash a heavy ashtray into their head and kill them. And then after its over, or someone else pulls them off, they 'snap' out of it, and sometimes freak out, "Oh my god, what did I do!?!". Survival instincts.