Actually, it places the burden on all equally.
No it doesn't.
The less money a family/individual makes, the higher the tax burden, thanks to the 9% Sales Tax. More and more Middle Class families/individuals are living check-to-check, thanks to flat wades that haven't kept up with inflation for the last three decades. Much of their expendable goes to necessities and many of those necessities would be taxable under Cain's tax plan.
According to the Department of Labor, a "typical average family" uses over 12% of their income for food. Now for simplicity, let's say their household income is the national average of $50,000. So, this family spends $6,000 on food in a year. With the 9% Sales Tax, they'll pay $540 in taxes on their food, that's a little over 1% of their income or now a total tax rate of 10%. A family whose household income of $250,000 also spends $6,000 for food and also pays out an extra $540 in taxes. That translates into .002% of their income, or now a total tax rate of 9.002% That purchase of a basic necessity translated into a almost a full 1% increase in the Middle Class's tax rate. But the wealthy family who is five times richer realized a .002% increase in their tax rate. Equality?
Now typically a family making $250,000 probably spends more on food than the family making $50,000. But to equal the sales tax's effect on their income, the wealthier family would have to spend the unrealistic total of $30,000 on food annually. Unless everyone in the family weighs 400 pounds, that's a whole lot of food.

The wealthy come no where near the spending totals of the Middle Class, when comes to spending as a percentage of their expendable income. Necessities spending makes up a higher percentage of a Middle Classes expendable income than it does for the wealthy.
I'm sorry, that placing "the burden of all equally" is not a truism at all.