Zoning is only a small part of the problem. Even if you zoned a bunch of new land today, if you let the private, free market have its course, then what do you think will be built on that land? Highly unaffordable luxury flats/houses, because that is what leads to the highest profit margins for the private sectors builders. And those flats will be bought up by investors or wealthy individuals to create more unaffordable rent.
That’s the core issue, individual private sector interests are not aligned to be altruistic interests for the good of society. They want to maximise profit, nothing more. Hence, you need someone willing to build houses and sell them at a loss, so average people can afford housing again. Only the government can sell for a loss and remain in business.
Ergo, you can zone all the land you want, but if you only let private sector builders have it, then you’ll just get more and more unaffordable properties built, chasing rich foreign investors, tech millionaires, or pension funds.
This is the core issue with Thatcherism/deregulation/privatisation. An individual company’s profit margins don’t always align with the good of society, but society needs essential services (water, sewage, electricity, food, housing, defense). These things need to be provided to all citizens, urban and rural, but doing so doesn’t always guarantee a profit, so you can’t just leave it to the private sector only.