If everyone pours much of BI income into mortgages but the supply of housing stays limited, then the price of existing houses will just go up-- and much of the BI income will get eaten up by housing price inflation.
Supply is limited in large part because everyone wants to live in the same place (ie where there is lots of work). BI will change that too, allowing people freedom to move where they can afford to live without worrying whether there will be jobs waiting for them. The free market in action. The impact a BI will have on society means that many of the patterns we see now will be flipped on their heads.
