We don't have a nationwide housing shortage. UBI might relieve pressure by letting some people relocate away from the local shortages in strong labor markets.
Even when people have the meas to relocate, they are reluctant to do it. If the housing market was fluid enough that we could consider nationwide factors, localized high-rent regions like Seattle, Vancouver or Silicon Valley wouldn't even occur in the first place.
So with or without nationwide housing shortage, any income increase will still be captured by local landlords.
