Well you've introduced a different system of administration as someone has to assess and review the negative income tax based on personal circumstances like number of children, disabilities etc.
Most of this does not require human assessment, in fact the meagre amount of money saved currently by sanctioning people viewed as "playing the system" is vastly outweighed by the cost of the job centre apparatus itself which is why staff were given sanction targets.
Anyway, whatever money is saved you have a system which ensures literally everyone is better off?
Reduced administrative costs are used to help people and when the tax rate is lower you tend to have less avoidance and evasion, thus more tax revenue paradoxically. Just look at the income tax rates in the USA, they were reduced massively in the 20's and as a result tax revenue from the rich increased so much they ended up with a budget surplus. But people want to hit the rich with a high tax rate so much that they cut their nose off to spite their face.
As economist Thomas Sowell puts it, "do you want a symbolic high rate of income tax or actual increased tax revenue?".