As the name implies, products are taxed at every stage of production. Take autos as an example:

Ore in a truck has more value than ore in the ground, so the mining company can be assessed a VAT when they sell the ore to the steel mill.

Processed steel has more value than ore, so a VAT would apply.

Auto parts have more value than raw steel, so another VAT.

Assembled autos typically have more value than a collection of parts*, so a VAT may apply there, too.

In the end, you have all the complexity and corruption of the current tax system, with the added disadvantage that the taxes at different stages of production are hidden (stealth taxes). All you see is the final price, not all of the taxes paid as part of that price. IMO: A VAT is the worst of both worlds.

While I'd love to see either a flat income tax or a national sales tax in lieu of an income tax, my leanings are towards the flat tax. As long as the 16th Amendment is in place, it'd only be a matter of time before we'd have a sales tax AND an income tax. All it would take is some sort of emergency to get Congress to enact a "temporary tax" (like the one on long distance calls that was passed to pay for the Spanish-American War and is still on the books).

The chances of repealing the 16th Amendment are virtually nill. Over 40 states have income taxes of their own, so unless the repeal amendment specifically allowed states to keep their income taxes, there's no way you could get 38 states to ratify the amendment.

Scrapping the current monstronsity of a tax code in favor of a simple flat tax would be a better alternative, IMO. However, I seriously doubt it will ever happen in my lifetime.

But then, I was surprised when the Berlin Wall fell. I'd love to be surprised again.

*If you go to a parts store and buy all of the parts needed to assemble a car, you'll end up paying several times what an assembled car costs. However, that's because you're buying the parts one at a time. The same isn't true for auto manufacturers.