The federal funds come from taxpayers. Poverty occurs unevenly across the country and across time. Although the national economy can be in good shape, the economy of any one state can be in recession with high unemployment.
Using federal funds for these programs accomplishes several things. It enables wealthier states to help states that have more poverty than wealth. It enables states with stable and growing economies to help states with economic problems.
Because poverty is a local problem, alleviating it requires local solutions. Having many pilot programs enables states to develop lots of approaches which can then be applied in other locations with similar problems.