You are quite correct that the overhead of most government programs is relatively very small.
But look at your numbers....12% of the population on SNAP, 20% of the population on Medicaid, etc etc.
What would it really cost us to just pay the equivalent cash to everybody, and then raise the taxes to offset the costs on people who don't need it?
We are already paying for--piecemeal and very inconveniently to be sure--much of what we'd want a UBI to give us. It probably would cost us more in taxes than what we are paying for now, but it wouldn't be an apocalyptic increase. The delta of spending is not as big as what one would initially think.