Adding a simple floor to the tax rate would solve much of the regressiveness. Nobody would pay taxes on their first $40k (or whatever number works), and then a

Adding a simple floor to the tax rate would solve much of the regressiveness. Nobody would pay taxes on their first $40k (or whatever number works), and then a flat rate above that. The floor could even be done as a prebate to gain some social safety net benefits. Every citizen is given $tax_rate * $40k every year, doled out as monthly payments, and pays a flat tax rate on all income.