This narrative that it hurts the poor is just not true. You get a prebate for basic consumption. It only hurts the poor who spend beyond their means on luxury goods, which is a hopeless situation anyways. (hurts is a poor term, because the cost of goods might not go up at all even with the tax included due to reasons stated elsewhere)

If anything, it allows the poor to pay less tax and save more of their paycheck if desired. It puts the choice in their hands.

Before it is claimed that the poor don't pay tax now anyways - that is only true if you consider gross income to be representative of financial status. You can make an above U.S. average salary and still be poor depending on where you live. This system does not discriminate based on gross income. It's like a no-limit IRA that you can withdraw from at any time.