They'd die with the slaves too.

The Earth is the only place where humans can live. A tiny number of humans can just barely live in orbit really near the earth as long as people on the earth keep spending millions to regularly send up supplies.

Problems that would have to be solved before humans could live somewhere else:

• Growing food
• Getting water
• Producing oxygen and getting rid of CO2
• Surviving radiation
• Surviving in a different gravity
• Repairing anything
• Manufacturing anything

Growing food is the obvious one. Even on Earth at 1G with ideal sunlight and low radiation, there has never been a successful closed biosphere. Surely you'd have to perfect closed biospheres on Earth before trying anything outside of earth, and then hope nothing goes wrong. When something goes wrong with the biosphere experiments on Earth they just open the door (or more often cheat and pretend it's still working while sneaking in food / oxygen from outside). And, even if you could get a closed biosphere to work, it would be the blandest vegan diet imaginable. To have any variety in your diet you'd need a massive, complex biosphere.

Water, oxygen and CO2 it's the same problem. Sure, we have an idea of how to recycle them in theory. But, in practice it's much more difficult. On the ISS they recycle about 80% of the water. Seems pretty good, but that means they still need deliveries of 6000 to 9000L of water per year, and that water is used for oxygen. On Earth, you can't lose water. The worst that can happen is that it escapes into the atmosphere where the atmosphere and gravity trap it, and it eventually returns to the ground in the form of rain. On Saturn or Jupiter water released into the atmosphere wouldn't escape into space -- but humans couldn't live on Saturn or Jupiter. Everywhere else the atmosphere is to thin or too hot, or the gravity is too weak to prevent water from escaping. So, even if you could get orders of magnitude more efficient at recycling water, and almost never have leaks, eventually you'd need a resupply.

Radiation is another huge one. The earth is protected by its magnetic field and thick atmosphere. Astronauts in the ISS are still mostly protected by that field because they're orbiting close enough, but they lose the protection of the atmosphere. 1 week on the ISS is like 1 year of background radiation on Earth. And, that's your best case. Go anywhere else and you will be cooked by radiation. The astronauts who did a quick 1 week jaunt to the moon were probably OK, but for actually living elsewhere you'd need a lot more protection. Maybe you could do that if you lived underground, but say goodbye to the idea of living in a dome or something.

Then there's gravity. Humans evolved to live in 1G. Astronauts who spend even just a few months in zero G often have permanent problems as a result. And, that's fully grown adults whose bodies were formed in 1G environments. Who knows what would happen in childbirth, or to a baby's development in anything other than 1G.

Finally, repairing and manufacturing. The modern world is very specialized, and often repair parts are made in a factory on the other side of the world. Electronics fail, and they'd fail a lot more in space where they'd be exposed to radiation. You could probably make a small facility in space that could repair basic electronics, but if a computer chip failed, there's no way you could make a semiconductor fab on another planet. Even on Earth it's a thing so specialized that it's only done in a handful of countries. 3d printing is cool and all, but it is extremely limited. Even the finest setting on the most advanced machine is very coarse compared to what can be done in specialized factories. You're also very limited in the kind of "filament" you use. Even if you use a metal filament, you can't make something much more complex than a wrench, and that wrench wouldn't even be like a good wrench which is made from heat-treated steel. So, you couldn't really live a modern life on another planet, but you also couldn't live a 17th century life where windmills were the most advanced devices around, because you wouldn't have wind, or flowing water, or trees to built things with, or anything else.

If humans really wanted to be a multiplanetary species, and were willing to spend absurd sums of money over decades to support a base on another planet while it got up to speed, then eventually, it might be more-or-less sustainable, as long as it had the ability to capture asteroids and so-on. Even then, life there would probably suck compared to life on Earth. Even compared to an earth ravaged by wars, climate change, etc.

The slaves are eating the cricket bars in the other vault

Those domes better be rocket proof. Or just rock proof.

Also, they need customers.