To @mmascari 's point, a dollar is basically not a dollar throughout the country. Land owners pass on their additional costs for prime land and taxes to their tenants, and businesses pass on their additional costs from taxes and their landlords to consumers. Eemployers have to then pay more to try to maintain a certain standard of living so there’s actually someone around to employ… and they pass that cost right on to their consumers again. In the net, 1) your dollar has less buying power than elsewhere, and 2) you are probably squeezing less buying power out of your employer than people elsewhere, even if you’re making numerically more dollars.
For example, using the BEA’s 2015 statistics on regional price parities, if you live somewhere in California, you have about 80% of the buying power of someone in Oklahoma.
It’s not necessarily “bluer” states that are depressed – it’s an interplay of employment opportunities, real estate costs, tax rates, and so on – but blue states do get hit pretty hard.
Personal opinion: the notion of a VAT is not based on any notion of fairness or economic theory; it’s simply convenient to the government. High taxes are distributed throughout the chain of materials and labor, basically disguising where your money is going. That makes it very politically convenient, because while prices are high, it’s hard for any angry voter to articulate why or who’s to blame. It coerces materials suppliers to collect the tax for the government, which is also convenient, because those vendors have no incentive to cheat on taxes for their customer, and it puts the accounting burden on them instead of on any government office.
VAT is a great way to steal money from your people on the cheap. But if that’s all you want to accomplish, we could instead look to tax methods in places like China, where they just make you pay taxes in advance on what you’re allowed to sell in the coming year. In any capitalist system, there’s already an index of a good’s total cost on society: it’s price. VAT accomplishes nothing of true economic value that cannot be accomplished by a simple sales tax.
If you want a solution to economic inequality, the answer is also simple: tax the rich more. If they were rich enough to surrender U.S. citizenship – for truly, the U.S. will get its citizens’ tax money, no matter where they’re living – then they were already rich enough to hide it, re-invest it, incorporate it, or find a loop-hole.
(I admit, that works only on a federal level: specific states still charge more, which incentivizes billionaires to move from, say, New Jersey to Florida, even if they still have to pay Uncle Sam all the same.)