Why are federal taxes less regressive than state taxes?
One of the better explanations for the regressivity of state taxes is as a natural political consequence of majority voting for the lawmakers who enact taxes.
Why would federal taxation be less regressive under that model? Because voter turnout is higher for federal elections (and voters are more informed about these elections) than is the case in elections involving state and local officials.
Since voter turnout and voter knowledge about elections is highest among higher income voters, voters who vote in federal but not state elections and voters who are well informed about federal but not state elections, will have lower incomes on average. It follows that federal elected officials should tend to be more concerned about the well being of low income voters than state and local officials. This concern translates into federal tax policies that are more progressive than state and local tax policies.