One more positive from your post that you didn't cover...
is that, when the government spends less, the economy grows, and more people get hired, thereby decreasing the unemployment rate.
Also, a flat tax would mean that, everyone would have to pay something, even if it's just a few dollars. That would make the people creating taxing policy to be a lot more careful with their tax bills, nobody would be asking to raise taxes on anyone, which would, again, lead to less fear in the economy, and companies and individuals would be free to invest with no fear of having their investments and any resulting wealth getting confiscated "for the good of the people".