Wouldn't that only work if there were some difficult-to-overcome mechanism (like a constitutional amendment) mandating a flat tax but letting the percentage var

Wouldn't that only work if there were some difficult-to-overcome mechanism (like a constitutional amendment) mandating a flat tax but letting the percentage vary easily? If you don't have that, a flat tax is going to lessen the desire to increase the flat tax rate, but it isn't going to do a thing to the desire to re-implement a progressive tax.