Suppose Alice makes $100,000 and Bob makes $20,000.
In a system that taxes at 5% up to $50,000 and 30% thereafter, the state gets a total of $18,500 from Alice and Bob.
In a system that taxes at 5% up to $50,000 and 40% thereafter, the state gets $23,500 from Alice and Bob.
In a system that taxes everyone uniformly at 25%, the state gets $30,000 from Alice and Bob. This is not a smaller number and 5/6ths of it is from Alice. In fact, you can use that money to give them each a $12,000 UBI, leaving Bob with an effective tax rate of -35%, delete all of the transfer programs that obsoletes and still have some left over for transit and uniforms.
You don't need it, it's already built in. The flat tax rate needed to serve as the implicit benefits phase out is already in the range as what you'd use in the high tax brackets in a progressive tax system with separate benefits phase outs.
If you want it to be more progressive you raise the flat tax rate and use the money to increase the UBI. If you want a less progressive system with lower taxes you do the opposite. Making it needlessly more complicated gains you nothing and costs you efficiency.
