You've just negated your own argument that home ownership is more affordable under BI. BI would increase disposable income across the board, increasing demand for purchased homes that is not necessarily coupled with an increase in supply. Prices go up overnight.

And home mortgages are low risk now - rates are about 3.5% which is among the lowest you can get for any loan, especially one multiple times higher than the borrower's yearly income over multiple decades, and any responsible person will be paying their rent long after they've switched their diet to PB&Js and ramen noodles. It's the first thing coming out of every check.