You might be interested to check out the Viennese model - Approximately 220,000 municipal flats and 200,000 subsidized dwellings form the backbone of Vienna's housing system, housing about 50% of the population.

Prices in Vienna are so much more affordable than in comparable European cities - Munich, Hamburg, Berlin to speak of Germany, not to say Madrid, Paris, Barcelone, Milano.

In Singapore it seems 80% of people live in public housing https://en.wikipedia.org/wiki/Public_housing_in_Singapore though I can't speak as to what the effect is on its housing market

Own nothing, be happy

UBI is perfect tool to make citizens obey to state. You'll always vote for your breadwinners.

Why, instead of centralised planned economy that failed ans killed millions people many times in history, not just lowering taxes and let people to decide how spend their capital individually? Game theory applied on UBI sounds really like an ugly idea.