The market is willing theoretically, but practically with high property values there's more incentive to build tons of smaller units since they'll sell for more in aggregate. This happened in my city, where there's a distinct lack of family-sized apartments in the downtown core. Only older buildings from the 80s prior to recent real estate booms built decent sized units suitable for families.

Well I guess that's the problem with having failed to produce housing supply for decades, until the balance of the market got so far out of whack that pressure for smaller units is that high. Tokyo built both housing and infrastructure to increase the viable land to live in striking distance to the commercial core, and so that's not an issue (although typical apartment sizes for family homes included are much smaller across the board because of the premium on space).

To me, it's a scenario of pick your poison - continue to be unaffordable because society is not willing to accept the consequences of its failures, or eat the consequences for a brighter future. In cities like SF, I don't see a world where it will ever get affordable if they insist that everyone needs to live in 1000+ sqft apartments, unless you plan to pack it to the gills with ultra-tall skyscrapers (never happening) or it becomes so undesirable to live there that people just stop moving there (unlikely, but given the rampant human rights violations it commits everyday to its denizens... well maybe that's the most likely scenario).

Aside, Americans don't know what small apartments even mean. The presence of super tiny Tokyo apartments is a great thing IMO, it means that people can still live centrally even if they aren't rich. I think a lot of people would happily accept a well-designed 200 sqft apartment over a 2-hour commute, if society gave them that option, since Tokyo residents do that en masse everyday.