At the very least housing could be mass produced if there werent so many regulations getting in the way.
Manufactured houses earned their bad reputation though. Many of them are/were junk. A lot of them are made by the same guys (and quality) who make trailer houses. Many city (suburban) codes, or HOAs will not let you put one up at all. This means that you don't see many of the quality ones. Most people are not actually qualified to judge quality of construction, some of them even today look nice for 10 years and then the maintenance nightmare begins: the parts are not standard home center sizes so it is a lot of labor to fix anything.
For most suburban houses you can take tens of thousands $$$ off the cost of new construction, get a good floor plan, and have your house built in 1/4th the time as regular construction. Anyone who is thinking about building their own house should look into this option (remember what I said about quality above though), but there are more energy efficient options that I think you should pay extra for even though it drives you back to site built.
Maybe it was this place: https://www.huf-haus.com/en.html
So, these homes lack character?
In the US, Sears used to sell homes in a similar fashion.
The problem with trying to do this in the US is the diversity of building codes across the country which limits the economy of scale significantly.
As for school, you could easily argue that we already have mass produced education. There is an abundance of low-grade colleges, pseudo-colleges and fake universities that charge fortunes (in debt of course) for an "education" that is worth about as much as grass clippings.
There already is mass produced housing too, they are mobile homes. Do you want to lift whatever local zoning regulation is preventing a mobile home park from popping up nextdoor to you?
And yes, the economy is broken if both parents must work.
But I don't think the analogy to cars or other goods is completely valid: You'd also have to mass produce the land to build the houses on, which, from what I know, isn't possible yet today...
Of course you can go another route and try to build many cheap apartments in a small amount of space. That's basically what has been done in Germany (both of them) in the 1950s and onwards: They were building many large, very dense apartment complexes with architecture optimized for easy construction and for providing living space for as many people as possible. (Typically implemented as high-rise "apartment towers")
Cities are still dealing with the after-effects of those projects today: The apartments are typically very small and far away from parks or playgrounds. Maintenance is slso lacking as the owners try to minimize cost. This has made them unattractive for almost everyone who can afford something better. The result of of course that the tenants are for a high part very low-income or "problematic" persons who couldn't get any other apartment. This creates an unsafe environment and makes the apartments even less attractive, leading to a downward spiral...
Modern urban planning had tried to learn from those disasters. We know today that "living quality" isn't just a luxury, it can have a direct effect on vandalism, the crime rate, etc.
In SF, zoning limits prevent you from building too high, and you have things like abandoned warehouses sitting unused because they are zoned for "light industrial" instead of residential.
And even IF your awesome new project to increase the housing supply follows all the zoning rules, it is likely to be blocked anyway. This is because the not in my back yard community will retroactively change the zoning laws to prevent the construction of new buildings.
And I'm not talking about governments preventing shitty buildings from being created. I'm talking about developers who want to build extremely high quality luxury apartments, while offering the community 30 percent of the units as rent controlled apartments and still getting blocked, because apparently some people prefer 100 percent rent controlled of a 5 story building instead of 30 percent of a 50 story building.
housing supply can be increased to a certain extent but it's not straightforward. increasing housing supply in marginal areas leads to untenable situations. increasing housing supply in high demand areas is incredibly difficult for many reasons, some of which are regulatory (and solveable) others are simply the hard fact that you can't add more square miles to the surface of the earth.
healthcare can't be mass produced. it is strictly limited by availability of medical facilities, doctors, nurses, and health care administrators.
education can't be mass produced. it is strictly limited by availability of educational institutions. the university is a smoldering ruin these days, if you hadn't noticed. its possible that alternative approaches to education might be a good way to dramatically increase the supply available. it's a conversation we need to start having as a society.
essential food products CAN be mass produced and they already are. increases in commodity prices are heavily linked to geopolitics, energy economies (processing, refrigeration, and distribution tend to dominate costs and those are all functions of energy price), and long established dietary habits. it would be much more efficient for people to eat 90% less meat than they presently do but good luck changing the habit on a mass scale.
It certainly is for livestock.