A consumption tax is inherently regressive. Those with smaller incomes must use a larger proportion of it on consumption. The wealthy will spend a comparatively tiny fraction of their income on tax and continue to amass vast piles of money.
Doesn't this assume the rich and poor are buying the same items and services at the same prices? Which is hardly the case.
A whole wheat or gluten free loaf of bread costs a lot more than your basic white loaf (Sorry actual celiacs).
A free-range natural chicken costs a lot more than the factory raised ones.
Organic produce costs more than your industrial farming equivalent.
File-minion costs several times per pound than ground chuck.
A luxury class car costs a lot more than a compact or full size car.
A sports car costs a lot of money and is hardly usable for most as the sole vehicle.
A haircut at a saloon costs several times what it would cost at the local barber.
If you want you can also tack on a luxury tax to higher end items and services as many states already do.