But it's totally doable btw. See China. They use eminent domain like a mofo.
1. We have expensive housing because we don't build enough.
2. We don't build enough because of anti-growth city regulations enacted by NIMBY politicians elected by NIMBY homeowners.
Corporate interests and billionaires aren't the ones that keep anything from getting built. They're your homeowner neighbors with lawn signs that say "NO ON EVERYTHING" each election season.
In a supply pinch, government subsidies just inflate home prices further, pouring more money into home sellers' pockets, the same way government-subsidized college tuition has poured more money into colleges' pockets. You can't solve a government-caused supply problem with government subsidies. Instead, you have to ask yourself the hard question - do I want much more housing? Do I want economically dynamic cities to grow, with all the problems that can bring? Most voters in these cities don't, and that's why we have the expensive cities we have. There's not enough to go around, so what supply there is goes to the highest bidder.
Now, regarding China - it relies heavily on private developers. The CCP learned decades ago that people just aren't motivated to work unless they own the rewards. This led Deng Xiaoping to transform China into an effectively capitalist economy ruled by a one-party corporate technocratic autocracy. The end result is that China is still owned by rich people, they're just rich people in the Communist Party. If you think money and power are uncomfortably close in the US, wait until you learn about the CCP! If the US government had the power of the corrupt Chinese political elites, Jeff Bezos could be disappeared for months (or forever) without any explanation whatsoever from anyone, and everybody would have to take it in stride. They can build infrastructure, yes, but it comes at a heavy price. And most people are kept out of the cities by the hukou system, which is NIMBYism on steroids.
You know you could buy a home with 0% down. The government could back the loans and have very low interest rates on these loans. It’s all possible - but we’re stuck in such a strong capitalistic mindset that we ignore other possible ways of running the country and imagining home purchases.
There’s also no reason we couldn’t have the government building beautiful and delightful buildings that are also attainable for everyday workers. It’s because we are stuck in our capitalistic mindset and so anti-government that we cannot imagine other ways of doing things.