You're not wrong, especially about "double the square footage for the same price". But that's why it's essential that the key to affordable housing isn't just connecting outlying suburbs by transit but also reevaluating zoning laws to fit more units in the same space.
For a simple example, look at one of the most livable and expensive (per sqft) cities in the world, Tokyo. A median family can afford to buy a single family house in the Tokyo metropolitan region. This works because the entire Tokyo region, including transit-connected suburbs, have very little restrictions on the type of housing that can be built, and where it can be built. ( Great article: https://www.curbed.com/2017/2/3/14496248/tokyo-real-estate-a... )
That model might not necessarily work perfectly for America, particularly because Tokyo is only increasing in population 1% per year and America's top cities are growing faster than that. But I guarantee thats a lot closer to a solution to the housing crisis than anything North America has produced.
For a simple example, look at one of the most livable and expensive (per sqft) cities in the world, Tokyo. A median family can afford to buy a single family house in the Tokyo metropolitan region. This works because the entire Tokyo region, including transit-connected suburbs, have very little restrictions on the type of housing that can be built, and where it can be built. ( Great article: https://www.curbed.com/2017/2/3/14496248/tokyo-real-estate-a... )
That model might not necessarily work perfectly for America, particularly because Tokyo is only increasing in population 1% per year and America's top cities are growing faster than that. But I guarantee thats a lot closer to a solution to the housing crisis than anything North America has produced.