The Federales overtax the States who are then forced to become beggars to get some of their money back but this is only remitted on the Federales terms. Strings attached. Chains attached.
Please bear in mind that one of the very few powers that the states have delegated to the feds, expressly via the Constitution, the specific power to regulate, tax and spend for where federal domestic policy is concerned is to run the US Mail Service. This is evidenced by the Constitution’s Clause 7 of Section 8 of Article I.
In other words, you can bet that most other federal social spending programs are unconstitutional, the federal funding for these programs being stolen state revenues that should never have left the states in the first place, and win most of your bets.
If low-information state lawmakers were to wise up put a stop to unconstitutional federal taxes, effectively eliminating an unconstitutional middleman, then the individual states would have much more revenues to spend on their respective citizens.