A UBI would increase any state budget by about 50%. I.e. in the US a UBI would cost about 2 trillion, with an overall budget of 4.
So what you are saying just does not add up. What you are describing would be correct if the UBI would be $100 per month vs $1000.
Yes, but taxes would be increased and benefits cut down commensurately. The net effect would be zero for the vast majority of tax payers as well as states. It's really just a technicality designed to reduce bureaucracy in the distribution of welfare benefits and not some mechanism intended to increase income transfers as a whole.
UBI would replace significant parts of the current welfare system. How much do you think the system we have costs to run?
In Finland, the lowest level of unemployment benefit is about €550 per month (there are other benefits on top of that). What I'm suggesting is that unemployment benefits and any other benefits someone might receive instead of unemployment benefits such as state-paid minimum pensions be slashed by an amount equal to the UBI. The average and high-income people would technically receive UBI as well but their taxes would be hiked commensurately. There would be no change in the take home earnings for most people.