In a nutshell, you defeat your own purpose. “Encouraging the construction of new, cheaper homes in the places they are needed most.” is just wrong because homes aren’t needed at all: people are. The rich get richer because the poor work for them and buy their stuff. Buying stuff instead of making it oneself is the core problem. People leave the land to take jobs in order to have more money to buy more stuff. If buying stuff is more expensive than making it, then people can use their UBI for useful things, rather than for useless things. If you notice your chart, the UBI paid to people goes open-loop. Therein is the problem with that type of setup.
Any funding of UBI needs to come from sales tax in order to inform the consumer of the real cost of buying instead of creating things. Then, and only then, can we also ask, “What are people for?”, and start leading toward a world where people are encouraged to contribute to their place rather than to exploit every resource for money. Money isn’t the problem: people having blind belief in the Invisible Hand Job is. Evil is always an action taken based on an unquestioned belief. In the case of LVT, it’s the blind belief that people are inherently good and useful. They are not unless we teach them and encourage them to be. In order to do that with money, they need to know the real costs of using money, and that only occurs at the purchase point, not at the earning point (income tax is just stupid).
All of the advantages of the Rich come from what the rest of us grant them with our money and time, and we do so when we buy their stuff and accept their wage slavery.