What makes people think housing should be affordable in the "most wanted" locations? You can't physically fit unlimited people in a small area.
You can certainly fit a lot more people in most major Western cities, without even much difference in lifestyle. Simply allow people to build what they want on their land, within reason. We've seen this in New Zealand, where recent law changes have allowed townhouses (terraced housing, with shared walls but otherwise freehold) and many many townhouses are being built everywhere.
Most houses are still standalone houses, no one is forcing you to develop your property, but if every 20th section is turned from a single house into 6 townhouses, a lot more people are able to fit into a smaller space while still having a comfortable, quiet home in a good location.
Our intertenancy walls have good soundproofing, enforced by regulations, so you don't really hear your neighbours. You can pay more for a standalone house, or less for a house with shared walls.
Although before WFH (and maybe even afterwards), the world's top billionaires were insisting engineers live within 20km of them so they can work at their companies. Industries like tech (and finance, and defence) heavily cluster, leading to certain cities/regions getting horrendously expensive.