The US don’t have a federal VAT equivalent but each state has its own purchase tax, Alaska has 0% or at least it did way back in the ’90’s.
We don’t need Brexit to change the VAT rate, we just can’t go below 15% which is the standard rate throughout the EU. It was our government alone that decided to raise the rate to 20% so nothing to do with the EU. The Tories put VAT on to energy supply at 8%, Labour then tried to scrap it but because it was put on after 1991 it meant it could only be reduced to 5%. Boris, Gove and others now blame the EU but in reality it was our wonderful (disabled unfriendly) Conservative government who caused all the problems.
On the subject of VAT how many remember that when it was first introduced it was supposed to be luxury items only.