This blather about embedded taxes is mainly nonsense. Sure in a theoretical sense that economists love it can possibly get removed but all that does is to allow businesses to externalize costs onto the public that they have no business not paying for.
An example of this is the mileage tax that trucking companies pay for using certain roads. I live near a gravel pit. The left-turn off the local State Route that turns onto the road that leads to the gravel pit has to be repaved about every 2 years because the heavy trucks and their tandem trailers tear up even the hardest concrete that they can lay down. Why should we, the local residential tax-payers who's vehicles require a resurfacing once a decade and a repaving every 3 decades, have to absorb the cost that the gravel pit is "externalizing" onto society?
Essentially that amounts to a subsidy to the business. And we know that subsidies to businesses adversely distort the free market and encourage businesses to change their business plans in ways that take advantage of this subsidy.
So in this case, it is very clear that the added mileage tax imposed on the trucks is simply removal of a subsidy, "fair" tax economists would call this an "embedded tax".
Most of the "embedded taxes" are taxes of exactly this sort.
Most products that are the subject of these "embedded taxes" do not sell overseas or compete with overseas goods. In fact those that do, are given special subsidies to do so -effectively offsetting the "embedded tax" impact on competitiveness. Thus the "fair" tax doesn't improve international competitiveness in any meaningful way. But it DOES increase the tax burden of individual citizens.
Nor would the "fair" tax increas the instream of foreign companies manufacturing in the USA. Why? Because most other countries similarly subsidize those corporations that export into the USA. And it isn't the tax rate that limits manuracturing in the USA, it is the cost of land and labor. Since being in NAFTA would let these companies sell into the USA anyway, what you would see is an increase in MFG plants in Mexico. And in fact you DID see that for a while. But with the PRC coming on line with strong MFG capabilities, even the tax benefits of NAFTA did not offset the labor costs, so you see the MFG moving from Central America to SE Asia.
IOW, this claim that "embedded taxes" will be "fixed" by the "fair" tax. is a solution in search of a problem. It is marketing spin and nothing more. Hollow claims - also known as bullshit.