You're missing the point. The reason why housing is expensive is not the lack of available land. The reason why housing is expensive is due to the fact that a lot of people want to live in and around very specific locations and don't want to waste time commuting to and from those locations.
The other half of the answer is that (in short) we've created a set of legal structures to prevent land owners from building the amount of housing that the market would otherwise build on their own land.
The scarcity, and thus value, comes from excluding people.
There actually is a lack of affordable land. Rural land has been amalgamated by the agriculture companies, timber companies, and government. Buying rural land usually has to be done in large acreages and it is still expensive.