If there is one house per person then approximately every person gets a house, because almost everyone is willing and able to pay more for their first house than even a very wealthy person will pay for a second one. If there are 1.5 houses per person then you will have to work quite hard at being homeless.
This is wildly incorrect, wealthy people are far more likely to be able to afford and willing to pay more for excess housing than an average person. Especially if they can turn around and rent those houses at a profit.
Houses are an asset. Wealthy people in search of assets will buy the houses and rent them back to you. Or they will invest in companies that buy the houses and rent them, or banks that buy them and mortgage them for a profit.
