We have a negative income tax through EIC. It's too small to matter though.

It's not too small to matter. For the worst case scenario of a mother of 3+ who's working several part time jobs, it pays on average around $7K. In most of the country that is rent for a year. And since someone getting an EIC is likely in government housing as they'll qualify for it, it could then be groceries for a year. Only as they qualify for EIC, they are likely on SNAP, and this money is somewhat freed up for things besides food and housing.

So for many it is too small to matter either because they don't have dependents, don't work enough, or work too much. But it's actually a near damned perfect incentive to keep people working and trying to find better jobs while keeping them out of abject poverty. Likely the best anti-poverty tool the US government has blindly stumbled upon ever.

Also worth noting, Milton Friedman advocated that in lieu of other poverty programs, because it gets rid of bureaucracy, leaves an incentive to work, and is less parent-like than existing methods.

The EIC is on top of the programs Friedman wanted to replace.