Why? Everybody would pay the same on anything they choose to buy. Rich people would pay more, because they buy more, and more expensive, things.
And of course you could exempt necessities. You wouldn't have to exempt food, because basic food would be free.
Besides, sensible economic policy would create jobs, which enable more people to buy stuff and pay the sales taxes. Do you want to optimize general well-being, or optimize fairness?
One advantage of the sales tax is that it would apply to imported and to domestically manufactured goods equally. And it should apply to services and to financial transactions.
John