Right, if you don't similarly fix the housing bottleneck, then nothing stops rents from just advancing to capture the additional UBI.

I think there's a general problem here, about the "how much you got?" economy -- increasingly many critical goods are charged for in a way that effectively eats up any gain in income. For example, college and health care -- you get hit with an obscenely high bill and they just figure out how much you can really afford and charge that.