It is the case now that imports are subsidized via tax rebates of one form or another to remove tax costs from them, making them more competitive here.
It is also the case that US goods are being anti-subsidized (is that a word?) with the penalty of included taxes...meaning importers can increase their price with no loss of market share to the extent that prices of domestic goods are inflated.
Importers have a double-tax advantage now.
Under the nrst, importers will have to pay the nrst, eliminating part of their advantage due to their tax subsidies of the home country.
And to help domestic business, US goods will become cheaper overseas by the amount of previously included taxes.
Import prices are unlikely to change - if they go up, that means that a very profitable market will be shrunk.
JMHO
Most of the studies I have read state that, due to exchange rate adjustments, any change in the trade balance would be very short term.