That’s a pretty decent approach. Until...
The folks from the states that have the “progressive” tax that find it’s really more “regressive” begin to leave that state. They move to the other states with the flat tax. Elect people that get a “progressive” system set up. Which becomes “regressive”, of course, over time. Move to next state. Repeat. Ruin state. Move on.
Sound familiar at all?
That’s not really a sustainable scenario to be realistically feared. They can’t do that to all 50 states in succession, because there just aren’t enough of them to do it, and if enough all moved to another state to change the tax system, the people who don’t want it can move to the state they left and switch the tax system there, so nothing would be accomplished.
People don’t move for the purposes of political activism in any great numbers anyway. They move for economic reasons, and any political changes are just collateral damage based on demographic shifts. If what you feared was a realistic scenario, then having a federalized government at all would be pointless, but it isn’t.