What you're describing is more like a negative income tax. As long as the tax brackets are narrow enough (or better yet: tax rate is a continuous increasing fun

What you're describing is more like a negative income tax. As long as the tax brackets are narrow enough (or better yet: tax rate is a continuous increasing function of income!) so that at no point does increasing youre before-benefit income reduce your total after-benefit income. With negative income tax, you have the problem of people cheating on their taxes to get free money, so it's often assumed that implementing it would require the abolition of cash.