UBI directly reduces inequality. That is mathematically true because it changes the distribution of income. However, I do agree that focusing funding on economic rent is the optimal way of funding UBI, especially via a land value tax, for UBI to have the greatest possible effect on inequality.
I've written more about this for the World Economic Forum: https://www.weforum.org/agenda/2017/04/extreme-wealth-inequality-alaska-model
I’m afraid that it would and there’s already empirical evidence to support it.
I usually reference a speech that Winston Churchill made to Parliament in which he said that people who lived on the south side of London had to pay sixpence each week in tolls to cross a bridge to get to work. It make not sound like much these days, but it was serious enough for the government to buy the bridge so that they could cancel the toll.
Churchill noted that, shortly after, rents on the south side went up by sixpence per week.
This is an example of how giving a known increase in income to everyone will accelerate inequality growth - UBI money would simply flow from the hands of the many into the hands of the few, which is why taxing economic rents is mandatory - it’s how you combat this rent-seeking behaviour.
There is not empirical evidence to support it. Here is some evidence.
In Lebanon, people were given unconditional cash grants comparable in size to basic income. Those above an elevation line got it, those below didn't. This created a natural experiment where the only variable was getting or not getting the money. Result? There was no effect on rents.
In the 70s experiment in the US, the cash resulted in a 4-6% increase in home ownership. That reduces upward pressure on rents.
In Mexico, I suggest just reading this next.
https://www.vox.com/policy-and-politics/2017/9/20/16256240/mexico-cash-transfer-inflation-basic-income
Also keep in mind that as long as the UBI is a flat nationwide rate, it essentially puts landlords in high CoL areas in competition with lower CoL areas.
There’s nothing but empirical evidence to support what I said.
The first example you gave was from an experiment that gave money to some people. This is a non-UBI and therefore sub-sufficient for proving the viability of an actual UBI. It’s the same mistake that they made in Finland.