US $414,000 per apartment was the original bid? Something has gone terribly wrong with your civilization.
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I think about the Isla Maciel slums where I used to volunteer. They're on the outskirts of Buenos Aires, and although I'm not familiar with any official statistics, I think the average daily income is under a dollar per person per day, with significant variation above and below that level. Some of the roads are dirt while others are paved, and the buildings are mostly somewhat ramshackle houses made of hollow brick with corrugated iron roofs. It's sort of similar to some of the neighborhoods I lived in as a kid in the US before I moved into a trailer park.
Despite this astonishing level of income, there is no homelessness (though there is elsewhere in Buenos Aires), and almost nobody rents. This is because people build their own houses. The most common material is hollow ceramic brick, the kind that's a latticework of thin red-clay walls; you have to scavenge or buy these https://articulo.mercadolibre.com.ar/MLA-821163523-ladrillo-... at a cost of about AR$6000 (US$50) per pallet of 144 bricks, which works out to about 35¢ per brick. The poorest people instead build with wood, like people in the US. (We haven't had an earthquake here during human habitation.)
If you do the figures, you can see that a generous 7 m × 3 m wall contains about US$130 worth of bricks, plus a smaller and cheaper amount of sand and cement. You can build a 49 m² house from four of these walls (US$520) plus 49 m² of corrugated steel, which if you have to buy it https://articulo.mercadolibre.com.ar/MLA-799438818-chapa-aca... is about AR$24000 (US$200). Putting these parts together into an actual building envelope typically takes a semi-skilled laborer a week or two, and most people either do it themselves or have their sons, boyfriends, or husbands do it, since they don't have any money to hire someone else. Adding a toilet, a sink, a bidet (we are not barbarians, after all), some PVC pipes for water and sewer, and a kind of shitty electrical installation (hopefully with at least a circuit breaker) might bring the total out-of-pocket cost close to US$1000.
You might note that US$1000 is significantly less than US$414000.
Now, Isla Maciel is a dangerous place. Everyone has lost family members either to gang violence or to police violence. I wouldn't advise visiting without knowing anybody there any more than I'd advise trying to visit the US without a visa; people there laugh about the stories of the tourists who mistakenly wandered into their neighborhood and got robbed. I'm not holding it up as an ideal of human civilization. But I'd much rather have a house in Isla Maciel than a park bench in Los Angeles or a rat-infested motel room in Solana Beach.
And I don't think the violence there is a result of a lack of enforcement of building codes, as someone will no doubt attempt to argue in response to this comment. Rather, both the insecurity and the freedom to build your own house result from the lawlessness of the neighborhood, which in turn proceeds from a general feeling that the law establishes oppression rather than justice — a proposition with ample empirical support within the confines of Isla Maciel, in my view, as well as other similar slums in Buenos Aires. This in turn undermines officially recognized systems of land tenure, with the consequence that residents of Isla Maciel can often claim land by building on it, if that doesn't piss off the neighbors too badly.
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How much would building such a house in the US cost, if it were somehow allowed? Let's suppose the cost of labor is some US$30 per hour (https://www.ziprecruiter.com/Salaries/How-Much-Does-a-Constr... gives an average of US$16/hour with a range of US$9–23, but this doesn't include overhead, worker's comp, unemployment insurance, etc.) which works out to US$2400 for two person-weeks. So maybe the total cost is US$3400, including materials and labor. So the cost of labor isn't the problem. Something has gone terribly wrong with your civilization.
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I reread Laura Ingalls Wilder's Little House on the Prairie last month, and I was struck by the description of the building process. If we take the description in the book as factual (not everything in the book is, but I assume in this case Ingalls Wilder was doing her best) it took a couple of weeks for a skilled carpenter and an unskilled assistant to build the single-room log cabin which afterwards housed a family of five for a year, plus another few days for the fireplace. But this was using raw materials from nature — trees chopped down and hauled from the creek by horse-drawn wagon, mud mortar to hold the fireplace stones together, mud for the chimney. (The chimney later caught fire due to shoddy construction and nearly burned down the house, and a dropped-log accident nearly broke Ma's foot. Building codes and safety rules are important!) Presumably the family had an outhouse for defecation, although the book shrinks from even mentioning such matters.
She doesn't give dimensions for the house, but it seems to have been around 4 m × 5 m, some 20 m², less than half the size I described above. My own apartment is 40 m²; fortunately I'm spending the quarantine at my girlfriend's apartment, which is some 50 m². (The roof leaks, the pipes burst, the curtains billow from the wind even when the window is closed, and whoever installed the electricals was either an idiot or a homicidal maniac, but she had my refrigerator, you see…)
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How did we get from a situation where an average person could build a five-person house with four person-weeks of labor — 0.08 years' of per-capita GDP — without even the support of a manufacturing base to provide them with boards, bricks, and toilets, to a situation where an "affordable housing" unit costs 6 years' worth of the US per-capita GDP, and 7 years of the US median household income? That is, a median household in the US now needs to work for seven years to pay the cost of building a house, rather than two weeks. Half the population earns less even than that. When it comes to housing buying power, people in the US are three orders of magnitude poorer than 150 years ago, or than in the worst slums of Buenos Aires today. Something has gone terribly wrong with your civilization.
Some people might cite the cost of land (both the Isla Maciel residents and Ingalls Wilder's family simply took their land without paying for it), but consider https://www.landsofamerica.com/property/0.2-acres-in-Los-Ang..., 0.2 undeveloped acres for US$175000, about 20 km from downtown LA. In non-medieval units, that's 800 m², enough for 15 of the 49 m² single-story houses I described above, which works out to US$12000 per house; if you dig a basement, you could cut that to US$6000 per house, at some penalty to the construction cost. Moreover, if you could build a 15-story apartment building on half of that land (you can't, it's zoned industrial), it would hold some 100 apartments of 49 m² each, at a land cost of US$1750 per apartment. In a skyscraper you have to pour reinforced concrete slabs for floors, which isn't free, but at ground level it typically costs on the order of US$50 per square meter, which is only US$2500 for 50 m². $1750 + $2500 + $3400 = $7650 ≪ $414000! Something has gone terribly wrong with your civilization.
Some people might cite Baumol's cost disease: when productivity goes up, wages go up, and so goods that have fixed labor requirements become more expensive; Baumol's example is an hour of chamber quartet music, which continues to require four musicians for an hour, just as in 1787. (The article itself blames "union-level wages" for construction workers.) But that explanation would suggest that construction workers like Miguel Zamora could easily buy housing, and we know that's not true. Even if the whole workforce was earning the US$51 per hour cited for plumbers in the article, that would only add another US$2500 or so per dwelling to the numbers I calculated above.
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What if, instead of using ten-thousand-year-old technologies like log cabins and bricks cemented together with mortar, we used modern technology to build housing?
You might get something like the Hexayurt, which costs under US$500, can be built by one unskilled person in less than a day, and shows up by the thousands every Burning Man: http://hexayurt.com/ — although there are some fire safety concerns with the material, so stuccoing it might be advisable. That might double the cost.
High-cube 40-foot shipping containers cost about US$7000 (or much less, used) and can be stacked into buildings many stories high; they are watertight, laugh at earthquakes, and have 28 m² of floor area. For $414000 you could buy dozens of them, maybe hundreds.
Or you might get something like modern trailer houses; I don't know how much these cost to make, but you can get them used for US$20k–US$40k, full of amenities like gas stoves, showers, cabinets, glass windows all around, multiple bathrooms, electrical outlets in all the walls, and central heating, unheard of in both Ingalls Wilder's time and in Isla Maciel. But could we maybe sacrifice some of the outlets, and the heavy welded steel frame that allows you to move your house to a different trailer park, in exchange for ending homelessness?
Something has gone terribly, terribly wrong with your civilization.