It can't replace the whole benefit system so the only saving is a relatively small amount of adminstration costs. I doubt such an amount would be redistributed in such a way with a flat tax that literally everyone would benefit.
A negative income tax guarantees everyone a basic level of income based on personal circumstances like number of children, disabilities etc. that can replace the current benefit system where we have all these useless job centres distributing universal credit that do nothing other than try to save a few quid here and there by sanctioning people, getting rid of the job centres alone would have enormous cost savings.