> Prices, in fact, should drop with more demand and thus flexible supply adapting. Cheaper by the volume.
Housing isn't a flexible supply and isn't much cheaper by the volume (if anything, it can become more expensive because of the space).
Personally that's my biggest issue with UBI. If it's not taken together with incentive to build suburbs/other cities that will make people want to go further away... most of it will go toward rent because you will all compete for a better location (I don't know for you but I waste 2 hours a day to go to works, I could lower that to 30 minutes a day for less than 1000$ a month, that's for sure).
We already see this effect in the cities that attracted startups. They got higher wages (which can be seen as "basic income" essentially because there was already a similar job done for less money close to there), which made housing price to go much higher.