Taking people off the tax roll at this stage, at the lower end, will not necessarily reduce poverty. It will further reward people who have figured how to do aggressive tax planning. What happens when you raise wages is that you do get a multiplier effect with respect to consumer ability to sustain the economy.
You could make the argument that reducing taxes, or increasing the threshold at which one is taxed, would do the same thing. It would give you more purchasing power, but the multiplier effect is much greater in terms of raising wages. It reaches people who could actually spend more money, rather than people who are already at the edge and would be just using it to pay off debt.