The traditional income redistribution systems in the US are social security (from the young to the old), welfare (from the employed to the unemployed), and medicare (from the healthy to the unhealthy). The cost of these systems is $X + $Y + $Z. Costs are inflated by large bureaucracies put in place to enforce social mores as punitive measures against the poor ("piss in this cup or you don't get EBT this month"; "EBT is for buying cheez-puffs, not condoms").
If giving $X + $Y + $Z to everyone in the US would provide them with a better quality of life, then it makes sense to do that instead of managing separate programs.
Two significant additional benefits to a basic income are:
1. It fixes the problem of going from unemployed to employed-at-minimum-wage resulting in a net decrease in household income. It's a simple observation that punishing people for getting a job will decrease the total number of employed adults.
2. It enables the minimum wage to be much lower than the poverty line. The nation has collectively decided that an adult working full time should be entitled to to the basic necessities of life, and the cost of that decision is that jobs which are worth less than $7.25 simply aren't offered (or are only offered illegally). If everyone already makes enough to get by, then there's far fewer ethical problems with paying someone $3 an hour to sweep some floors or pick up garbage from a sidewalk.